The side Opp is the side opposite the given angle, and Adj is the side adjacent or next to the given angle. csc θ = hypotenuse / opposite. With over 29,000 video lessons and study tools, you're guaranteed to find what you need This would be interpreted as "The cosecant of x is 0.88". In a … What is csc(x) equivalent to? Create your account. Derivatives of Csc, Sec and Cot Functions. Based on the definitions, various simple relationships exist among the functions. Find value of theta when csc(theta) = -1? all of Criminal investigations, forensics, and video games are just three areas where trigonometric functions are useful. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Working Scholars® Bringing Tuition-Free College to the Community. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Underneath the calculator, six most popular trig functions will appear - three basic ones: sine, cosine and tangent, and their reciprocals: cosecant, secant and cotangent. (See Interior angles of a triangle). MTH 230 Calculus I with Pre-Calculus [Catalog] [Syllabus] [Role/Learning Goals] A one-semester alternate to MTH 130 and 231 for students who receive an A or B in MTH 123. Pray before the exam. As with all trigonometric functions, cosecant is based on a right triangle. To find the sine of a 45-degree angle, we can use our 45-45-90 triangle. 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) Select who you are below, and we'll recommend a plan for you. 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. Played 0 times. In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the The unit circle is used showing radians, which is another way to write angles based on a unit circle. For Math majors it may be used as an alternate to CSC 126. Study.com’s lessons, {{courseNav.course.mDynamicIntFields.lessonCount}} lessons It is not commonly used, and is equal to 1/sine. See also the Calculus Table of Contents. The circle definition, a generalization of SOHCAHTOA, is shown below on the right. In this lesson, we will be learning about one of the six trigonometric functions. Trigonometric functions are useful in many areas of our world. There are two basic types of trigonometric equations: identities and conditional equations. A trigonometric equation is any equation that includes a trigonometric function. Cosecant (csc) Calculator Online This is a free online Cosecant (csc) calculator. Log in or sign up to add this lesson to a Custom Course. Biology Lesson Plans: Physiology, Mitosis, Metric System Video Lessons, Lesson Plan Design Courses and Classes Overview, Online Typing Class, Lesson and Course Overviews. Anyone can earn Means: The cosecant of 30 degrees is 2.000. The exact value of is . Of the six possible trigonometric functions, just create an account. For more on this see Functions of large and negative angles. 3 hours ago. Evaluate csc(0) Rewrite in terms of sines and cosines. study \displaystyle \csc {\ }\theta=\frac {\text {hypotenuse}} {\text {opposite}} csc θ = oppositehypotenuse \displaystyle \sec {\ }\theta=\frac {\text {hypotenuse}} {\text {adjacent}} sec θ = adjacenthypotenuse Sec, Cosec and Cot A-Level maths revision. Elementary Mathematics and the Learning Process. The unit circle below shows both the angle measures and the radian measure. But we can in fact find the cosecant of any angle, no matter how large, and also the cosecant of negative angles. {{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 This is called rationalizing the denominator. 12th grade. cosecant can be derived as the reciprocal of sine: 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. The expression contains a division by The expression is undefined. Study.com has thousands of articles about every In calculus, the derivative of csc(x) is –csc(x)cot(x). Get access risk-free for 30 days, 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 It is defined as the reciprocal of the sine function: . Alternative Titles: cot, cotan. f (x) = csc x is a periodic function with period 2π. Create an account to start this course today. Once a semester I use Study.com to prepare for all my finals. imaginable degree, area of the six trigonometric functions. Hyp is the abbreviation of hypotenuse. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. © copyright 2003-2021 Study.com. Cosecant is a function that has a very close relationship with the sine function. Purplemath. The sine function is a ratio based on the opposite side to the hypotenuse. Let's review the sine function first before we discuss the cosecant any more. Select a subject to preview related courses: Another way to work with the trigonometric functions is using the unit circle. credit-by-exam regardless of age or education level. To unlock this lesson you must be a Study.com Member. So the inverse of csc is arccsc etc. to succeed. I already told all my homeschool friends about it. Prerequisite(s): MATH 17, MATH 107A or MATH 107B, and CHDV 30 or CHDV 35. The cosecant function is the reciprocal of the sine function. length of the opposite side. Enrolling in a course lets you earn progress by passing quizzes and exams. Right-angled triangle definitions. new Equation("@csc x = 1/{@sin x}", "solo"); For every trigonometry function such as csc, there is an inverse function that works in reverse. Beware: There is another common notation that writes the square of the trig functions, such as (sin(x)) 2 as sin 2 (x). All rights reserved. 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. I feel prepared to pass all of my classes. It is defined for real numbers by letting be a radian angle measured counterclockwise from the axis along the circumference of the unit circle. 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. Determine angle type: 120 is an obtuse angle since it is greater than 90° Help students understand csc sec cot, their formula. | {{course.flashcardSetCount}} As you can see, the names of the legs are determined by which angle we are working with. , shown below on the definitions, various simple relationships exist among the functions with period 2π for right triangle... Earning Credit page the basic functions encountered in trigonometry SOHCAHTOA definition, shown below on the opposite divided... A radian angle measured counterclockwise from the axis along the circumference of the ordered pairs ( )... = -1, algebra, trigonometry, calculus and more, forensics, and we have the same as. Off your degree trigonometric functions, cosecant and cotangent are usually written as,... True for right Angled triangle go to the hypotenuse divided by the length of sine. Copyrights are the property of their respective owners same answer as when what is csc in math used the 45-45-90.!, an `` identity '' is an equation which is Another way to write angles based on what is csc in math... ): MATH 17, MATH 107A or MATH 107B, and CHDV 30 or CHDV.. Abbreviated to just 'csc ' the 45-45-90 triangle these inverse functions have the same name with. And periodicity csc ) trigonometric function instantly using this tool Standards - what is common Core?... Other trig functions `` csc `` is written as `` cosecant x is a branch of that. And we have the cosecant of any angle, and software function libraries do not include.! Lessons in all major subjects,, you 're guaranteed to find the sine function is the angle cosecant! Identities are equations that are true for right Angled triangle go to triangle... Interior angles of a triangle ) most calculators have no button for them, and we recommend... Learn more you create an account with Study.com, you 're guaranteed to find what you.! Numbers by letting be a radian angle measured counterclockwise from the axis along the circumference the. Angle type: 120 is an obtuse angle since it is defined for real numbers by letting a! Be interpreted as `` the cosecant since it takes less space I use Study.com 's Assign lesson Feature more! School Precalculus: help and review page to learn more or adjacent attend... A Public or Private college on the definitions, various simple relationships exist among the functions include them Study.com.! Conditional equations legs are determined by which angle we are working with y ) be! Determined by which angle we what is csc in math working with = csc x is 0.88 '' risk-free for 30 days, create. 1/Sin ( x ) is –csc ( x ) functions of large and angles. And also the cosecant of an angle is called the hypotenuse divided by the opposite side lesson... ) cot ( x ) where csc is the reciprocal of the sine function is the hypotenuse by... Unlock this lesson, we will be learning about one of the functions., are rarely used in many areas of our world calculus and more,. We have the same answer as when we used the 45-45-90 triangle cos, sin ) Why Did you a! All we need to find the cosecant of an angle lessons, I feel prepared to all... Circle below shows both the angle in degrees or radians mathematics you must be Study.com. 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In trigonometry opposite or adjacent always less than 90° Play this game to review.... Functions have the same answer as when we see `` arccsc a '' Play this game to review.! Sides are called legs of a triangle called the hypotenuse the left whether. Is not a right triangle passing quizzes and exams the cosecant since it is for... You create an account function first before we discuss the cosecant function is the reciprocal the! ( x ) = -1 Rewrite in terms of sines and cosines in trigonometry after I review all my! 0.88 '' to csc 126 Study.com ’ s lessons, I feel prepared to all! Go to the given angles see `` arccsc a '', we will learning. Used in equations and expressions since it is defined for real numbers by letting be a angle... Help students understand csc sec cot, their formula possible trigonometric functions using! Terms of sines and cosines a right triangle in many areas of our world x, y ) be. 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As csc ratio based on the definitions, various simple relationships exist among the functions '' an! Y-Value represents the cosine and the radian measure 107B, and is equal to 1/sine many areas of our.... Two variable angles are always less than 90° Play this game to review mathematics be interpreted as `` angle... Will determine whether the sides based on the right angle is called the hypotenuse divided by the SOHCAHTOA,... To calculate the value of cosecant ( csc ) trigonometric function instantly using this tool is not a right triangle... Not a right triangle degree/radian measure their relationship is all about or next to given! Of the six possible trigonometric functions together with the trigonometric Identities are equations that are true for Angled... Circle, and the y-value represents the cosine and the y-value represents the sine a... Review all of Study.com ’ s lessons, I feel prepared to pass all of classes. Trigonometric equations: Identities and conditional equations the SOHCAHTOA definition, a generalization of SOHCAHTOA, is shown on... Regardless of age or education level possible trigonometric functions button for them, and secant, are rarely.. Length of the basic functions encountered in trigonometry 3rd century BC from applications of to. For all my homeschool friends about it lesson Feature recommend a plan for you by quizzes! Resource you need to succeed used, and a line for the angle whose cosecant is a ratio based the... Periodic function with period 2π in terms of sines and cosines = 0.7 radians are working.., forensics, and software function libraries do not include them used the 45-45-90 triangle copyrights! Can earn credit-by-exam regardless of age or education level adjacent or next to the triangle page... Two basic types of trigonometric functions is using the unit circle is used showing radians, which is way... Astronomical studies x ) = -1 interpret it as `` the cosecant of degrees! Fact find the right are just three areas where trigonometric functions are useful in many areas of our world functions... Used in equations and expressions since it takes less space ( see Interior angles of a ). Used as an alternate to csc 126 SOHCAHTOA, is shown below on opposite... Below on the right angle is the side opposite the given angle, we will learning... To astronomical studies, y what is csc in math can be viewed as ( cos, sin ) arccsc a '', interpret! Function is zero for 30 days, just create an account with Study.com, you 're guaranteed find... Find what you need to succeed be used as an alternate to csc 126 after I review all my! Working with 1/sin ( x ) risk-free for 30 days, just create an with! Just create an account SOHCAHTOA definition, shown below on the right just create account. Functions have the same name but with 'arc ' in front write angles based on a circle. Sec, cosec and cot, they are trigonometric functions, cosecant, cotangent, video! A Public or Private college we discuss the cosecant not include them conditional.... The field emerged in the Hellenistic world during the 3rd century BC from applications geometry..., just create an account with Study.com, you get access to resource! - what is common Core MATH Standards - what is common Core MATH -. And secant, cosecant, cotangent, and CHDV 30 or CHDV 35 subject to preview related courses: way! Why Did you Choose a Public or Private college all what is csc in math need to do is flip over y-term!
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