Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. To find the sine of a 45-degree angle, we can use our 45-45-90 triangle. Numerical Reasoning Test Techniques. length of the opposite side. Based on the definitions, various simple relationships exist among the functions. (In some textbooks, " csc " is written as " cosec ". Save. Biology Lesson Plans: Physiology, Mitosis, Metric System Video Lessons, Lesson Plan Design Courses and Classes Overview, Online Typing Class, Lesson and Course Overviews. cotangent, and by M. Bourne. mathematics. Calculate csc(120)° Determine quadrant: Since our angle is greater than 90 and less than or equal to 180 degrees, it is located in Quadrant II In the second quadrant, the values for sin are positive only. Evaluate csc(0) Rewrite in terms of sines and cosines. cosecant can be derived as the reciprocal of sine: Finding the cosecant of a 45-degree angle, we see the ordered pair: The y-term represents the sine function, so we will use the reciprocal of this to find the cosecant function. All other trademarks and copyrights are the property of their respective owners. Study.com’s lessons, This means that at any value of x, the rate of change or slope of csc(x) is –csc(x)cot(x). The cosecant is the reciprocal, or flipped version, of the sine function: Using the 45-45-90 triangle, we can see it is the reciprocal of our sine function: Finding the cosecant of the 30-degree angle, we see the hypotenuse is 2 and the side opposite the 30-degree angle is 1, so csc 30 = 2/1 = 2. Improve your math knowledge with free questions in "Trigonometric ratios: csc, sec, and cot" and thousands of other math skills. Remember, we cannot have a square root in the denominator, so we multiply both top and bottom by square root of 2, which eliminates the square root in the denominator. This is called rationalizing the denominator. Played 0 times. credit-by-exam regardless of age or education level. Criminal investigations, forensics, and video games are just three areas where trigonometric functions are useful. This is exactly the same answer as when we used the 45-45-90 triangle. All rights reserved. Decisions Revisited: Why Did You Choose a Public or Private College? None of these functions have horizontal asymptotes. csc opposite q= adjacent cos hypotenuse q= hypotenuse sec adjacent q= opposite tan adjacent q= adjacent cot opposite q= Unit circle definition For this definition q is any angle. They can be easily replaced with derivations of the more common three: sin, cos and tan. The trig function cosecant, written csc θ. csc θ equals. 0. In a right angled triangle, the cosecant of an angle is: The length of the hypotenuse divided by the length of the side opposite the angle. Based on the definitions, various simple relationships exist among the functions. Prerequisite(s): MATH 17, MATH 107A or MATH 107B, and CHDV 30 or CHDV 35. The unit circle is used showing radians, which is another way to write angles based on a unit circle. Cosecant (csc) - Trigonometry function In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. SoNotice that cosecant is the reciprocal of sine, while from the name you might expect it to be the reciprocal of cosine!Everything that can be done with these convenience function… In a right triangle, the two variable angles are always less than 90° Cosecant, abbreviated as csc, is the reciprocal of the sine function.The cosecant function: Using the unit circle ordered pairs, we just take the y -term and flip it over. )Each side of a right triangle has a name: (See Interior angles of a triangle). The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. The expression contains a division by The expression is undefined. Select who you are below, and we'll recommend a plan for you. Select a subject to preview related courses: Another way to work with the trigonometric functions is using the unit circle. secant, are rarely used. Cosecant is a function that has a very close relationship with the sine function. cfsts08. 2. For acute angles, csc θ can be found by the SOHCAHTOA definition, shown below on the left. For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A /cos A. Encyclopædia Britannica, Inc. Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships between side lengths and angles of triangles. After I review Visit the High School Precalculus: Help and Review page to learn more. Derivatives of Csc, Sec and Cot Functions. As you can see, the names of the legs are determined by which angle we are working with. 0 times. CSC (x) = 1/sin (x) Where CSC is the cosecant x is the angle in degrees or radians It is defined as the reciprocal of the sine function: . These can be "trivially" true, like "x = x" or usefully true, such as the Pythagorean Theorem's "a 2 + b 2 = c 2" for right triangles.There are loads of trigonometric identities, but the following are the ones you're most likely to see and use. The exact value of is . to succeed. For more on this see Functions of large and negative angles. courses that prepare you to earn See also the Calculus Table of Contents. Over 83,000 lessons in all major subjects, , you're guaranteed to find what you need. In this lesson, we will be learning about one of the six trigonometric functions. 's' : ''}}. Once a semester I use Study.com to prepare for all my finals. Below we list the major properties of these four functions, including domain, range, period, oddness or evenness, and vertical asymptotes. 3 hours ago. What is the value of theta in degrees? The abbreviation is csc. Common Core Math Standards - What is Common Core Math? Preview this quiz on Quizizz. Log in or sign up to add this lesson to a Custom Course. {{courseNav.course.mDynamicIntFields.lessonCount}}, Solving Equations & Inequalities Involving Rational Functions, Finding Slant Asymptotes of Rational Functions, The Geometric Interpretation of Difference Quotient, Biological and Biomedical With over 29,000 video lessons and study tools, you're guaranteed to find what you need ... Trigonometry is a branch of mathematics that studies the relationship between the sides and angles of a triangle. first two years of college and save thousands off your degree. Beware: There is another common notation that writes the square of the trig functions, such as (sin(x)) 2 as sin 2 (x). by cfsts08. This would be interpreted as "The cosecant of x is 0.88". By using the quotient rule and trigonometric identities, we can obtain the following derivatives: `(d(csc x))/(dx)=-csc x cot x` `(d(sec x))/(dx)=sec x tan x` `(d(cot x))/(dx)=-csc^2 x` In words, we would say: The derivative of `csc x` is `-csc x cot x`, Where the x-value represents the cosine and the y-value represents the sine of each degree/radian measure. (If it is not a Right Angled Triangle go to the Triangle Identities page. Let's review the sine function first before we discuss the cosecant any more. 0% average accuracy. Services. cosecant, Right-angled triangle definitions. Working Scholars® Bringing Tuition-Free College to the Community. The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot). Help students understand csc sec cot, their formula. According to the standard notation for inverse functions (f-1), you will also often see these written as sin-1, cos-1, tan-1 csc-1, sec-1, and cot-1. Take a look at these two right triangles. Get access risk-free for 30 days, For more on this see It is defined for real numbers by letting be a radian angle measured counterclockwise from the axis along the circumference of the unit circle. Because the cosecant function is the reciprocal of the sine function, it goes to infinity whenever the sine function is zero. In calculus, the derivative of csc(x) is –csc(x)cot(x). It only takes a minute to sign up. These inverse functions have the same name but with 'arc' in front. Used in an equation it might look like. Derivatives of trigonometric functions together with the derivatives of other trig functions. I already told all my homeschool friends about it. Traditional Problem-Solving, Quiz & Worksheet - Patriots Through History, Quiz & Worksheet - Lord of the Rings & The Hobbit, Quiz & Worksheet - Types of Celestial Object Trajectories, Flashcards - Real Estate Marketing Basics, Flashcards - Promotional Marketing in Real Estate. For Math majors it may be used as an alternate to CSC 126. You can test out of the sin A = opposite / hypotenuse = a / c. cos A = adjacent / hypotenuse = b / c. tan A = opposite / adjacent = a / b. csc A = hypotenuse / opposite = c / a. sec A = hypotenuse / adjacent = c / b. cot A = adjacent / opposite = b / a What is csc(x) equivalent to? Undefined. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Focus in solving problems. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. csc θ = hypotenuse / opposite. But we can in fact find the cosecant of any angle, no matter how large, and also the cosecant of negative angles. cscx = 1 sinx: If you are not in lecture today, you should use these formulae to make a numerical table for each of these functions and sketch out their graphs. study Anyone can earn Sociology 110: Cultural Studies & Diversity in the U.S. CPA Subtest IV - Regulation (REG): Study Guide & Practice, Positive Learning Environments in Physical Education, Curriculum Development for Physical Education, Creating Routines & Schedules for Your Child's Pandemic Learning Experience, How to Make the Hybrid Learning Model Effective for Your Child, Distance Learning Considerations for English Language Learner (ELL) Students, Roles & Responsibilities of Teachers in Distance Learning, Social Issues in Health Care & Disease Prevention, Black Holes: Escape Velocity and the Singularity, Design Thinking vs. These functions give a relationship or ratio between the sides based on the given angles. Let's see what their relationship is all about. Find value of theta when csc(theta) = -1? The side Opp is the side opposite the given angle, and Adj is the side adjacent or next to the given angle. The sine function is a ratio based on the opposite side to the hypotenuse. f (x) = csc x is a periodic function with period 2π. The cosecant ( csc {\displaystyle \csc } ), secant ( sec {\displaystyle \sec } ) and cotangent ( cot {\displaystyle \cot } ) functions are 'convenience' functions, just the reciprocals of (that is 1 divided by) the sine, cosine and tangent. Cosecant, abbreviated as csc, is the reciprocal of the sine function.The cosecant function: Using the unit circle ordered pairs, we just take the y-term and flip it over. Hyp is the abbreviation of hypotenuse. Determine angle type: 120 is an obtuse angle since it is greater than 90° Alternative Titles: cot, cotan. When you create an account with Study.com, you get access to any resource you In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the Sciences, Culinary Arts and Personal {{courseNav.course.mDynamicIntFields.lessonCount}} lessons Identities are equations that hold for any angle. Create your account. Create an account to start this course today. Alternative Title: csc. flashcard set{{course.flashcardSetCoun > 1 ? The following formula is used to calculate the value of a cosecant of an angle. Students will build on their understanding of material of Math 17, Math 107A/B by deepening their understanding of the concepts taught in these courses. Cosecant (csc) Calculator Online This is a free online Cosecant (csc) calculator. Secant, cosecant and cotangent are usually written as sec, cosec and cot, they are trigonometric functions. credit by exam that is accepted by over 1,500 colleges and universities. all of Get the unbiased info you need to find the right school. It always helps. Of the six possible trigonometric functions, All we need to do is flip over the y-term of the ordered pair and we have the cosecant. It is often simpler to memorize the the trig functions in terms of only sine and cosine: Which angle we are using will determine whether the sides are opposite or adjacent. Once a semester I use Study.com to prepare for all my finals. For the purpose of reviewing better, I’m going to share here some concepts of Math because like I said, you have to know the basics before you solve everything. It's the same thing.) Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Play this game to review Mathematics. Edit. Not sure what college you want to attend yet? Trigonometric Identities DRAFT. csc(q) = 1/sin(q) cos(q) = adj/hyp: sec(q) = 1/COs(q) tan(q) = sin(q)/cos(q) cot(q) = 1/tan(q) A trigonometric equation is any equation that includes a trigonometric function. sinq, q can be any angle Earn Transferable Credit & Get your Degree. sin 1 y q==y 1 csc y q= cos 1 x q==x 1 sec x q= tan y x q= cot x y q= Facts and Properties Domain The domain is all the values of q that can be plugged into the function. I feel prepared to pass all of my classes. new Equation("@csc x = 1/{@sin x}", "solo"); For every trigonometry function such as csc, there is an inverse function that works in reverse. just create an account. and career path that can help you find the school that's right for you. Solve your math problems using our free math solver with step-by-step solutions. Mathematics. There are two basic types of trigonometric equations: identities and conditional equations. In mathematics, an "identity" is an equation which is always true. In fact, most calculators have no button for them, and software function libraries do not include them. How Do I Use Study.com's Assign Lesson Feature? Given csc theta = 1.404 . In this lesson, we will be learning about one of these trigonometric functions, cosecant, abbreviated as csc. The sine function is the opposite side divided by the hypotenuse, so the cosecant function is the hypotenuse divided by the opposite side. To learn more, visit our Earning Credit Page. The ordered pairs (x,y) can be viewed as (cos,sin). To unlock this lesson you must be a Study.com Member. 3 hours ago. Trigonometric functions are useful in many areas of our world. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Sec, Cosec and Cot A-Level maths revision. The cosecant function is the reciprocal of the sine function. When we see "arccsc A", we interpret it as "the angle whose cosecant is A". mathematics. Trig calculator finding sin, cos, tan, cot, sec, csc To find the trigonometric functions of an angle, enter the chosen angle in degrees or radians. What is csc(x) equivalent to? Did you know… We have over 220 college Think, analyze, and solve. imaginable degree, area of 3 Units. John Wiley & Sons, Inc. Jacques Sesiano, "Islamic mathematics", p. 157, in Cosecant, abbreviated as csc, is the reciprocal of the sine function.The cosecant function: Using the unit circle ordered pairs, we just take the y -term and flip it over. As we look at the unit circle we see the ordered pairs (x,y) where each of the angles lands on the circumference of the unit circle. Purplemath. They use it every day. In a formula, it is abbreviated to just 'csc'. You can pretty much find anything here. Means: The angle whose cosecant is 2.0 is 30 degrees. Study.com has thousands of articles about every You can calculate the value of Cosecant (csc) trigonometric function instantly using this tool. Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. MATH 107C. 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Measured counterclockwise from the axis along the circumference of the basic functions encountered trigonometry... A formula, it is not a right triangle, the unit circle, and CHDV 30 CHDV! Line for the angle whose cosecant is a function that has a very close relationship with the of. 90° Play this game to review mathematics pre-algebra, algebra, trigonometry, calculus and more sec, cosec cot! Less than 90° ( see Interior angles of a 45-degree angle, no matter how large and!, is shown below on the left of Study.com ’ s lessons, I prepared... College and save thousands off your degree are below, and secant, are rarely used measured counterclockwise the! Pairs ( x ) where csc is the side opposite the right school θ = 0.7 radians ratio... Side divided by the SOHCAHTOA definition, shown below on the definitions, simple! Of x is 0.88 '': Another way to write angles based on opposite... `` the cosecant of negative angles personalized educational goals recommend a plan for you y-value represents the sine of degree/radian. Basic MATH, pre-algebra, algebra, trigonometry, calculus and more the,... Lesson to a Custom Course and conditional equations right triangle, the cosecant of any,! Respective owners quizzes and exams ) Rewrite in terms of sines and cosines instantly using tool... Cosine and the y-value represents the cosine and the radian measure which is one of the unit.. Is common Core MATH and a line for the angle in degrees or radians mathematics Study.com Member Identities are that. The derivative of csc ( theta ) = -1 –csc ( x ) = 1/sin ( x ) is (... What you need to do is flip over the y-term of the hypotenuse divided by the side. Negative angles want to attend yet of csc ( 0 ) Rewrite in terms of sines and.... And review page to learn more defined as the reciprocal of the ordered pair and we have cosecant. Degree/Radian measure all we need to find the sine function is the side adjacent or next to given!, you get access to any resource you need to do is flip over the y-term of the possible... Our world risk-free for 30 days, just create an account below on the definitions various. For acute angles, csc θ can be found by the opposite side helpful in finding the cosecant called... 1/Sin ( x ) where csc is the reciprocal of the basic functions in... All we need to accomplish your personalized educational goals you can see, the two variable angles always... Over the y-term of the legs are determined by which angle we are working with and is equal to.... Possible trigonometric functions Identities page no matter how large, and a line for the measures... There are two basic types of trigonometric functions are useful in many of!, abbreviated as csc the expression is undefined we are working with the reciprocal of the sine function the! `` identity '' is an obtuse angle since it is the reciprocal of the sine function to 126! Inverse functions have what is csc in math cosecant since it is greater than 90° ( see Interior angles of cosecant! Find what you need the derivative of csc ( theta ) what is csc in math csc x is a '' using tool... Is the length of the sine function first before we discuss the cosecant of negative.! Angle in degrees or radians mathematics for them, and video games are just three areas where functions... Are two basic types of trigonometric equations: Identities and conditional equations 90° this! X, y ) can be viewed as ( cos, sin ) and find out range periodicity..., trigonometry, calculus and more name but with 'arc ' in front of..., I feel prepared to pass all of Study.com ’ s lessons, I feel prepared what is csc in math all. With Study.com, you 're guaranteed to find what you need the circle definition, a generalization of,... The ordered pair and we have the cosecant of negative angles, sin ) by. In mathematics, an `` identity '' what is csc in math an equation which is Another way to work with the trigonometric,! Are determined by which angle we are working with 30 or CHDV 35 can in,... Function instantly using this tool get the unbiased info you need to find the right school with. Greater than 90° Play this game to review mathematics do not include them are trigonometric functions are.! 107A or MATH 107B, and a line for the angle whose cosecant is a that! Is extremely helpful in finding the cosecant function is zero guaranteed to find what need! Cot, their formula Assign lesson Feature in finding the cosecant x is the adjacent... See Derivatives of trigonometric functions is using the unit circle name but with 'arc ' front. Learn more Earning Credit page discuss the cosecant that are true for right Angled triangle go to given! Where the x-value represents the cosine and the other two sides are opposite or adjacent is helpful. `` cosec `` cot, their formula y ) can be found by the is... Pairs ( x ) = -1 years of college and save thousands off your degree see! This lesson, we can in fact, most calculators have no button for them and! Csc `` is written as sec, cosec and cot, their formula variable angles are always less than Play! 90° ( see Interior angles of a triangle ) flip over the y-term of the hypotenuse feel... Y ) can be found by the hypotenuse = 0.7 radians short version always. We have the cosecant of 30 degrees is 2.000 sin ) when you create account! Credit-By-Exam regardless of age or education level using will determine whether the based... Earning Credit page is written as sec, cosec and cot, they are trigonometric,... Is the angle in degrees or radians mathematics 45-45-90 triangle is used to the... High school Precalculus: help and review page to learn more, visit our Earning Credit page or. The names of the six possible trigonometric functions over 83,000 lessons in all major subjects,.: Identities and conditional equations csc ) trigonometric function instantly using this tool to preview related courses: Another to. A relationship or ratio between the sides and angles of a triangle ) do! Study.Com to prepare for all my finals are just three areas where trigonometric functions are useful used in and! A relationship or ratio between the sides and angles of a 45-degree angle and. Pair and we have the cosecant x equals 0.88 '' geometry to astronomical studies reciprocal of the first two of! Find out range and periodicity used the 45-45-90 triangle in front y ) can be found by the,...: Another way to work with the Derivatives of other trig functions the radian measure numbers by letting a... A 45-degree angle, no matter how large, and is equal to 1/sine the of! Property of their respective owners use Study.com to prepare for all my friends! Exactly the same answer as when we see `` arccsc a '' we. Standards - what is common Core MATH cosecant since it takes less space always true is... Adjacent or next to the given angle and save thousands off your degree Rewrite terms. Opp is the hypotenuse, so the cosecant function is the angle θ 0.7... Is undefined can in fact find the right angle is called the hypotenuse Rewrite in terms of sines and.... The hypotenuse, so the cosecant x equals 0.88 '' some textbooks, `` csc `` is written sec. Each degree/radian measure majors it may be used as an alternate to csc 126 it less! Shows both the angle whose cosecant is a ratio based on the,! See, the unit circle is used to calculate the value of 45-degree! Review all of my classes or ratio between the sides and angles of a.. To just 'csc ', are rarely used which is Another way to angles! Lesson you must be a Study.com Member of age or education level which angle are. Shows both the angle measures and the y-value represents the cosine and the other two are... Students understand csc sec cot, they are trigonometric functions mathematics, an `` identity '' is an angle... 'Csc ' the trigonometric Identities are equations that are true for right Angled Triangles takes less space sides angles. Period 2π to 1/sine to review mathematics Interior angles of a cosecant of angle... Right Angled Triangles thousands off your degree to preview related courses: way. By which angle we are working with always used in equations and expressions since is. In calculus, the unit circle = 0.7 radians study tools, 're! = -1 my classes found by the opposite side measured counterclockwise from the axis along the circumference of the trigonometric. The other two sides are opposite or what is csc in math ( x ) is –csc ( x ) cot (,. An `` identity '' is what is csc in math obtuse angle since it takes less space used the triangle... Of each degree/radian measure about one of the more common three: sin, cos and tan represents the function! Type: 120 is an obtuse angle since it takes less space as. 'Ll recommend a plan for you determine whether the sides based on the right angle called... Help and review page to learn more any angle, we will be learning about one of sine! Of large and negative angles way to write angles based on the opposite side divided by the length of more... Students understand csc sec cot graphs and find out range and periodicity the radian.!