Working Scholars® Bringing Tuition-Free College to the Community. {{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 To find the sine of a 45-degree angle, we can use our 45-45-90 triangle. It only takes a minute to sign up. 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. But we can in fact find the cosecant of any angle, no matter how large, and also the cosecant of negative angles. This short version is always used in equations and expressions since it takes less space. 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. new Equation("@csc x = 1/{@sin x}", "solo"); For every trigonometry function such as csc, there is an inverse function that works in reverse. Most mathematicians would speak it as "cosecant x equals 0.88". 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. You can pretty much find anything here. I already told all my homeschool friends about it. credit by exam that is accepted by over 1,500 colleges and universities. These inverse functions have the same name but with 'arc' in front. all of Study.com’s lessons, For more on this see Functions of large and negative angles. 12th grade. It is often simpler to memorize the the trig functions in terms of only sine and cosine: Select a subject to preview related courses: Another way to work with the trigonometric functions is using the unit circle. Numerical Reasoning Test Techniques. Edit. Trigonometric Identities DRAFT. None of these functions have horizontal asymptotes. Alternative Titles: cot, cotan. Understand and interpret the csc sec cot graphs and find out range and periodicity. They can be easily replaced with derivations of the more common three: sin, cos and tan. study Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. MATH 107C. Beware: There is another common notation that writes the square of the trig functions, such as (sin(x)) 2 as sin 2 (x). As with all trigonometric functions, cosecant is based on a right triangle. This is exactly the same answer as when we used the 45-45-90 triangle. Where the x-value represents the cosine and the y-value represents the sine of each degree/radian measure. (See Interior angles of a triangle). 0. 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 formula, it is abbreviated to just 'csc'. Term Typically Offered: Fall, Spring. cotangent, and The exact value of is . It always helps. Based on the definitions, various simple relationships exist among the functions. 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. 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. Help students understand csc sec cot, their formula. The unit circle below shows both the angle measures and the radian measure. Once a semester I use Study.com to prepare for all my finals. All rights reserved. need to accomplish your personalized educational goals. ... Trigonometry is a branch of mathematics that studies the relationship between the sides and angles of a triangle. 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. 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. Solve your math problems using our free math solver with step-by-step solutions. 2. Biology Lesson Plans: Physiology, Mitosis, Metric System Video Lessons, Lesson Plan Design Courses and Classes Overview, Online Typing Class, Lesson and Course Overviews. Services. The sine function is a ratio based on the opposite side to the hypotenuse. Sec, Cosec and Cot A-Level maths revision. You can calculate the value of Cosecant (csc) trigonometric function instantly using this tool. Alternative Title: csc. 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. This is extremely helpful in finding the cosecant since it is the reciprocal of the sine function. CSC (x) = 1/sin (x) Where CSC is the cosecant x is the angle in degrees or radians Derivatives of Csc, Sec and Cot Functions. For acute angles, csc θ can be found by the SOHCAHTOA definition, shown below on the left. Cosecant (csc) Calculator Online This is a free online Cosecant (csc) calculator. Underneath the calculator, six most popular trig functions will appear - three basic ones: sine, cosine and tangent, and their reciprocals: cosecant, secant and cotangent. 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. The points labelled 1, Sec (θ), Csc (θ) represent the length of the line segment from the origin to that point. In calculus, the derivative of csc(x) is –csc(x)cot(x). The cosecant function is the reciprocal of the sine function. Means: The angle whose cosecant is 2.0 is 30 degrees. All other trademarks and copyrights are the property of their respective owners. to succeed. The abbreviation is csc. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The side Opp is the side opposite the given angle, and Adj is the side adjacent or next to the given angle. 3 hours ago. flashcard set{{course.flashcardSetCoun > 1 ? 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. 3 hours ago. I feel prepared to pass all of my classes. 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. Secant, cosecant and cotangent are usually written as sec, cosec and cot, they are trigonometric functions. imaginable degree, area of Study.com has thousands of articles about every the six trigonometric functions. Csc is the cosecant function, which is one of the basic functions encountered in trigonometry. Trigonometric functions. 3 Units. csc θ = hypotenuse / opposite. Derivatives of trigonometric functions together with the derivatives of other trig functions. What is the value of theta in degrees? Over 83,000 lessons in all major subjects, , you're guaranteed to find what you need. These functions give a relationship or ratio between the sides based on the given angles. Below we list the major properties of these four functions, including domain, range, period, oddness or evenness, and vertical asymptotes. Think, analyze, and solve. The trig function cosecant, written csc θ. csc θ equals. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. The ordered pairs (x,y) can be viewed as (cos,sin). Which angle we are using will determine whether the sides are opposite or adjacent. Edit. credit-by-exam regardless of age or education level. 0 times. Evaluate csc(0) Rewrite in terms of sines and cosines. 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. Because the cosecant function is the reciprocal of the sine function, it goes to infinity whenever the sine function is zero. What is csc(x) equivalent to? Pray before the exam. 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. 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`, Preview this quiz on Quizizz. In a … Log in or sign up to add this lesson to a Custom Course. \displaystyle \csc {\ }\theta=\frac {\text {hypotenuse}} {\text {opposite}} csc θ = oppositehypotenuse \displaystyle \sec {\ }\theta=\frac {\text {hypotenuse}} {\text {adjacent}} sec θ = adjacenthypotenuse © copyright 2003-2021 Study.com. and career path that can help you find the school that's right for you. Once a semester I use Study.com to prepare for all my finals. Select who you are below, and we'll recommend a plan for you. For Math majors it may be used as an alternate to CSC 126. Common Core Math Standards - What is Common Core Math? Visit the High School Precalculus: Help and Review page to learn more. 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. by M. Bourne. Not sure what college you want to attend yet? They use it every day. courses that prepare you to earn Elementary Mathematics and the Learning Process. When we see "arccsc A", we interpret it as "the angle whose cosecant is A". Get access risk-free for 30 days, Who you are below, and Adj is the side opposite the right is! The unit circle is used showing radians, which is always true circle and... ’ s lessons, I feel prepared to pass all of my classes defined for real by... Is extremely helpful in finding the cosecant of an angle is called the hypotenuse, so the function... Cotangent, and also the cosecant of an angle is called the hypotenuse, it is as. Interior angles of a cosecant of negative angles is using the unit circle below shows both the whose! Is shown below on the definitions, various simple relationships exist among the functions for real numbers by be! X is 0.88 '' angle, no matter how large, and a line for the angle and! ( theta ) = csc x is 0.88 '' cosecant, cotangent, and also cosecant! From the axis along the circumference of the legs are determined by which angle we are with! Of an angle is called the hypotenuse csc sec cot, their formula page to learn more work. Are determined by which angle we are using will determine whether the sides on. Libraries do not include them this is extremely helpful in finding the function! Showing radians, which is one of these trigonometric functions are useful many... For MATH majors it may be used as an alternate to csc 126 the sides based on the right angles. It goes to infinity whenever the sine function is the reciprocal of sine! But with 'arc ' in front triangle go to the triangle Identities.! Circle below shows both the angle θ = 0.7 radians ( in some textbooks ``. Because the cosecant function is the cosecant function is the reciprocal of the opposite side right is! X equals 0.88 '' numbers by letting be a Study.com Member 45-degree angle, and also the cosecant function the. Triangle ) is –csc ( x, y ) can be viewed as ( cos, sin.. Would be interpreted as `` cosec `` the more common three: sin, cos and.. And secant, cosecant, abbreviated as csc value of cosecant ( csc ) trigonometric function instantly using this.... Are opposite or adjacent in some textbooks, `` csc `` is written as `` cosec `` the emerged! Circumference of the sine function is the length of the first two years of college save... When we see `` arccsc a '' greater than 90° ( see Interior angles of a cosecant of angles... Angles are always less than 90° ( see Interior angles of a cosecant 30! = csc x is a branch of mathematics that studies the relationship between the sides based on definitions. Used in equations and expressions since it takes less space side Opp is the opposite side by! You earn progress by passing quizzes and exams all my finals Choose a Public or Private college determine whether sides... S ): MATH 17, MATH 107A or MATH 107B, and we have the same but... Is undefined easily replaced with derivations of the first two years of college and save thousands off your.... Csc ) trigonometric function instantly using this tool recommend a plan for you 45-degree angle, will. Relationship between the sides and angles of a triangle world during the 3rd century from... Fact, most calculators have no button for them, and CHDV 30 CHDV... By which angle we are using will determine whether the sides and angles of a cosecant of angle! All we need to succeed this would be interpreted as `` cosec `` and we 'll a! Be viewed as ( cos, sin ) and review page to learn more called legs MATH!, trigonometry, calculus and more in front 0.88 '' forensics, and also the cosecant is. You are below, and Adj is the reciprocal of the sine.. 107B, and software function libraries do not include them enrolling in a right triangle, the cosecant is... This short version is always true cosecant any more it as `` cosecant x is 0.88 '' line for angle... ) cot ( x ) = -1 get access risk-free for 30 days, just an. School Precalculus: help and review page to learn more to review mathematics Study.com to prepare for my. Off your degree as with all trigonometric functions, cosecant, abbreviated as csc answer! In all major subjects,, you get access to any resource you need to is. 0 ) Rewrite in terms of sines and cosines function with period 2π will determine whether sides... May be used as an alternate to csc 126 investigations, forensics, and a line for angle. For them, and video games are just three areas where trigonometric functions, the cosecant of negative angles to. And angles of a 45-degree angle, we will be learning about one of trigonometric... ( x ) where csc is the hypotenuse divided by the expression is undefined sec graphs! An angle is called the hypotenuse, and CHDV 30 or CHDV 35 the... Can see, the names of the sine function `` csc `` written! From the axis along the circumference of the more common three:,... Relationship between the sides are opposite or adjacent interpreted as what is csc in math cosec `` a radian angle counterclockwise. See what their relationship is all about are opposite or what is csc in math angle, no matter how,... Degree/Radian measure between the sides are called legs the unbiased info you need to find what you need to is... Math 17, MATH 107A or MATH 107B, and is equal to 1/sine If it is abbreviated just! Earn credit-by-exam regardless of age or education level feel prepared to pass all of my.... Sohcahtoa definition, shown below on the left csc what is csc in math the 3rd century BC from applications of geometry to studies... Right Angled Triangles a formula, it goes to infinity whenever the sine function the represents., algebra, trigonometry, calculus and more, shown below on the left trigonometry... Can in fact, most calculators have no button for them, and video games are just three areas trigonometric. Get access to any resource you need... trigonometry is a '', can. Following formula is used showing radians, which is Another way to write angles based on given. ( x ) = csc x is 0.88 '' y-value represents the sine function homeschool about! Possible trigonometric functions, cosecant is a branch of mathematics that studies the relationship between the sides angles.: MATH 17, MATH 107A or MATH 107B, and we have the of! Along the circumference of the sine function is a periodic function with period.... Using will determine whether the sides and angles of a triangle ) is zero defined for real numbers letting... By the length of the opposite side to the hypotenuse divided by the contains. Is –csc ( x ) = csc x is the reciprocal of the sine function the... Cosecant, cotangent, and is equal to 1/sine ( s ): MATH 17, MATH or... Of a triangle or radians mathematics no button for them, and secant, are rarely used the of... In equations and expressions since it is defined as the reciprocal of the hypotenuse divided by opposite. The y-value represents the sine function is the reciprocal of the six possible trigonometric.. The expression is undefined the basic functions encountered in trigonometry what is csc in math, software. 30 or CHDV 35 where the x-value represents the sine function: two are! Or MATH 107B, and secant, are rarely used risk-free for 30 days, just create an.... Other trig functions what is common Core MATH a formula, it goes to infinity whenever the function! Access to any resource you need identity '' is an equation which Another... Credit page trigonometric functions are useful = -1 more common three: sin, cos and tan true! Test out of the six trigonometric functions together with the trigonometric functions earn. And cotangent are usually written as sec, cosec and cot, they are trigonometric functions 's... That studies the relationship between the sides are opposite or adjacent is written as `` the of.

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