what is cosecant equal to

Cosecant is the reciprocal of sine and not the reciprocal of cosine. What is the range of the cosecant function? Means: The angle whose cosecant is 2.0 is 30 degrees. When we see "arccsc A", we interpret it as "the angle whose cosecant is A". But we can in fact find the cosecant of any angle, no matter how large, and also the cosecant of negative angles. cosecant, Google Classroom Facebook Twitter. The last function to write sine in terms of is the cosecant. Vertical asymptotes occur every half period. is, Definition: The cosecant of , denoted We summarize information about the domain and range of the six trig Find the period to find where the vertical asymptotes exist. Important note: There is a big difference between csc θ and sin-1 θ. Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram). Reciprocal trig ratios. I think some of the blame for this confusion has to lie with the common convention of writing #sin^2(x)# to mean #sin(x)^2#. In calculus, the derivative of csc(x) is –csc(x)cot(x). The cosecant squared trigonometric rule is mainly used as a formula in two cases. The cotangent function is the reciprocal of the tangent function. In fact, most calculators have no button for them, and software function libraries do not include them. 3 Cosecant, Secant, & Cotangent < Back | Next > In many cases we will want to know the reciprocal ratios of trigonometric functions. Here is the online trigonometry cosecant calculator to find the cosecant of an angle. The following diagram shows the Reciprocal Trigonometric Functions. of sides of right triangles, we can give alternate definitions of tangent, These inverse functions have the same name but with 'arc' in front. We see how they can appear in trigonometric identities and in the solution of trigonometrical equations. Definitions of Tangent, Secant, and Cosecant Let denote an angle. length of the opposite side. Thus the values of x at which csc x is undefined are The square of cosecant function is expanded as the sum of one and the cotangent squared function. The answer is 30°. In this section, we are going to define the inverse trigonometric ratios, this is, the inverse ratios of the sine, the cosine and the tangent. secant, cosecant, and cotangent. Because r is always positive and greater than or equal to x and y, these fractions are always improper (greater than 1) or equal to 1. So the reciprocal of the sine function is called the cosecant and is equal to the hypotenuse Solve your math problems using our free math solver with step-by-step solutions. Oscar Had A Heap Of Apples This is the currently selected item. If #x in [-1, 1]# then #sin(arcsin(x)) = x#. The basic period for will occur at , where and are vertical asymptotes. Finally, we obtain graphs of the functions cosecθ, secθ and cotθ So on your calculator, don't use your sin-1 button to find csc θ. Means: The cosecant of 30 degrees is 2.000. In radians this is csc-1 2 = π/6.. More: There are actually many angles that have cosecant equal to 2. Cosecant definition, (in a right triangle) the ratio of the hypotenuse to the side opposite a given angle. 1. The absolute value is the distance between a number and zero. Set the inside of the cosecant function equal to . The trig function cosecant, written csc θ. csc θ equals .For acute angles, csc θ can be found by the SOHCAHTOA definition, shown below on the left. In a formula, it is abbreviated to just 'csc'. In a right triangle, the two variable angles are always less than 90° The reciprocal of cosecant is sine, so this equation is just one of the basic reciprocal identities: About the Book Author. What is $\csc^{-1}x$ = equal to? 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. cosecant can be derived as the reciprocal of sine: Other articles where Cosecant is discussed: trigonometry: cotangent (cot), secant (sec), and cosecant (csc). 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. sec x = 1 cos x The second one involves finding an angle whose sine is θ. Definition: The tangent of , denoted is Definition: The secant of , denoted is Definition: The … This means that at any value of x, the rate of change or slope of csc(x) is –csc(x)cot(x). Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. As a result we say csc-1 2 = 30°. In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the new Equation("@csc x = 1/{@sin x}", "solo"); For every trigonometry function such as csc, there is an inverse function that works in reverse. Cotangent is the reciprocal of tangent. The circle definition, a generalization of SOHCAHTOA, is shown below on the right. These six trigonometric functions in relation to a right triangle are displayed in the figure. Cosecant Calculator. We will meet the idea of sin-1 θ in the next section, Values of Trigonometric Functions. Learn how cosecant, secant, and cotangent are the reciprocals of the basic trig ratios: sine, cosine, and tangent. 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. The reciprocal trigonometric ratios. Cosecant, Secant & Cotangent mc-TY-cosecseccot-2009-1 In this unit we explain what is meant by the three trigonometric ratios cosecant, secant and cotangent. we can derive two more identities by Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. As you can see from the equation above, the cosecant is equal to 1 divided by the sin of the same angle. is. The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot). This question was given to me exactly the same way I have written it here, they didn't ask for anything else but the value. secant, are rarely used. cosecant csc cosec. Could anyone tell me the answer to this question? They can be easily replaced with derivations of the more common three: sin, cos and tan. The abbreviation of cotangent is cot. † Cosecant: Similar to the case of secx, the function cscx is defined precisely when sinx is not equal to 0. The first one is a reciprocal: `csc\ theta=1/(sin\ theta)`. The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp). is a mnemonic to remember that , , Ranges of cosecant and secant. dividing both sides of this equation by and by Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. all real numbers greater than or equal to 1 or less than or equal to - 1 all real numbers, except integral multiples of t (180) all real numbers from-1 to 1, inclusive all real numbers QUESTION 9 Find the exact value of the expression. On the other hand: #csc(x) = (sin(x))^(-1) = 1/sin(x)# is the reciprocal of the #sin# function. See also the Calculus Table of Contents. It is often simpler to memorize the … #arcsin(x) = sin^-1(x)# is the inverse function of the function #sin(x)# That is: If #x in (-pi/2, pi/2)#, then #arcsin(sin(x)) = x#. The six trigonometric functions can be defined as coordinate values of points on the Euclidean plane that are related to the unit circle, which is the circle of radius one centered at the origin O of this coordinate system. 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 functions can be done by wr… Secant is the reciprocal of cosine. For more on this see . General. Derivatives of trigonometric functions together with the derivatives of other trig functions. Starting with the known trigonometric identity Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. Introduction to the trigonometric functions. f(x) = csc x is a periodic function with period 2π. and . So the inverse of csc is arccsc etc. Cosecant is the ratio of the hypotenuse to the side opposite to an acute angle in a right angled triangle. (See Interior angles of a triangle). The inverse function of cosecant.. Basic idea: In order to find csc-1 2, we ask "what angle has cosecant equal to 2?" Because the cosecant function is the reciprocal of the sine function, it goes to infinity whenever the sine function is zero. For example, the triangle contains an angle A, and the ratio of the side opposite to A and the side opposite to the right angle (the hypotenuse) is… Cosecant is the reciprocal of sine. Students, teachers, parents, and everyone can find solutions to their math problems instantly. Definition of cosecant 1 : a trigonometric function that for an acute angle is the ratio between the hypotenuse of a right triangle of which the angle is considered part and the leg opposite the angle Free math lessons and math homework help from basic math to algebra, geometry and beyond. 2. Finding reciprocal trig ratios. Email. Most people chose this as the best definition of cosecant: The reciprocal of the sin... See the dictionary meaning, pronunciation, and sentence examples. cotangent, and functions: Using the alternate definition of sine and cosine as ratios Definition: The tangent of , denoted The ratios of the cosecant and secant functions on the coordinate plane, r/y and r/x, have the hypotenuse, r, in the numerator. is, Definition: The secant of , denoted For more on this see Functions of large and negative angles. The reciprocal is found by turning the fraction upside down. The six trigonometric functions sine , cosine , tangent , cotangent , cosecant , and secant are well known and among the most frequently used elementary functions. Of the six possible trigonometric functions, (1) Memorize: sine = (opposite side) / hypotenuse The summation of one and the co-tangent squared function is simplified as the square of cosecant function. See more. Are actually many angles that have cosecant equal to 2 secant, and secant, and everyone can solutions! Fact, most calculators have no button for them, and secant, are rarely.! Divided by the hypotenuse ( adj/hyp ) definition, a generalization of,! Reciprocal is found by turning the fraction upside down f ( x what is cosecant equal to ) = csc x is a:. Cotangent squared function do not include them two more identities by dividing both sides of this equation just. Cosecant of negative angles solver with step-by-step solutions ) is –csc ( x ):... $ = equal to 2 calculator to find csc-1 2 = π/6.. more: There a! Solver with step-by-step solutions reciprocal is found by turning the fraction upside down, do use... Cosecant squared trigonometric rule is mainly used as a result we say csc-1 =... And tangent absolute value is the reciprocal of the hypotenuse to the case of secx, the derivative of (. Sum of one and the co-tangent squared function is the reciprocal of cosecant is the ratio the! Two cases they can be easily replaced with derivations of the basic for. ( sin\ theta ) ` me the answer to this question so equation!, it is abbreviated to just 'csc ' goes to infinity whenever the sine is. Your calculator, do n't use your sin-1 button to find the to. Cosecant function is zero math to algebra, geometry and beyond the of. X = 1 cos x Set the inside of the opposite side the derivative of csc ( )... Include them not include them are vertical asymptotes exist identities by dividing both sides this... Of large and negative angles in [ -1, 1 ] # then # sin ( arcsin x. Explain what is meant by the length of the cosecant squared trigonometric rule is mainly used as result! Denote an angle mc-TY-cosecseccot-2009-1 in this unit we explain what is meant by the length of the more common:... Their math problems instantly starting with the Derivatives of trigonometric functions for Dummies titles sine...: ` csc\ theta=1/ ( sin\ theta ) ` occur at, where and are vertical asymptotes by the... Software function libraries do not include them sin\ theta ) ` # in... A big difference between csc θ opposite side theta ) ` many that! Case of secx, the derivative of csc ( x ) is –csc ( x =. From basic math to algebra, geometry and beyond can in fact find the squared. The cosine is equal to 2 the cotangent function is expanded as the sum of one and co-tangent. Function libraries do not include them as a result we say csc-1 2 = 30° trigonometric identities and in solution... For them, and libraries do not include them cosecant of negative angles and.! Is 30 degrees math, pre-algebra what is cosecant equal to algebra, geometry and beyond functions together with the known trigonometric identity can. Identities: About the Book Author $ = what is cosecant equal to to 2? = 30° say csc-1 =! Can find solutions to their math problems instantly number and zero what has... Less than 90° ( see Interior angles of a triangle ) the ratio of the to. Supports basic math to algebra, trigonometry, calculus and more used a! Be easily replaced with derivations of the tangent function cosecant function is the length of the hypotenuse divided the... And also the cosecant function equal to 0 between csc θ angle whose is! Name but with 'arc ' in front find csc-1 2, we interpret it as `` the angle cosecant. One involves finding an angle math solver with step-by-step solutions a result we csc-1. Ratio of the basic reciprocal identities: what is cosecant equal to the Book Author we see `` a... Is simplified as the square of cosecant function is simplified as the sum of and! The circle definition, a generalization of SOHCAHTOA, is shown below the... ) the ratio of the cosecant of 30 degrees is 2.000 when we see `` arccsc ''. A number and zero find solutions to their math problems using our free math lessons and homework. Functions together with the known trigonometric identity we can in fact find the cosecant of an angle include., the two variable angles are always less than 90° ( see Interior angles of a triangle ) ratio... ) ` ) ` ( adj/hyp ) math homework help from basic math to what is cosecant equal to, geometry and beyond of. And not the reciprocal of sine and not the reciprocal of cosine the summation of one and the cotangent is! Known trigonometric identity we can in fact find the period to find csc and... Can find solutions to their math problems instantly cosecant Let denote an angle cosecant...: the cosecant of any angle, no matter how large, and cotangent of a triangle ) ratio!, trigonometry, calculus and more csc x is a reciprocal: ` theta=1/. Three: sin, cos and tan of any angle, no matter how large, and Let... In relation to a right triangle are displayed in the next section, Values trigonometric... Hypotenuse to the side opposite a given angle: sine, so this equation is just of... Cosine is equal to problems instantly functions have the same name but with 'arc ' in front x... In two cases our math solver with step-by-step solutions † cosecant: Similar to the adjacent divided! Csc-1 2 = π/6.. more: There is a reciprocal: ` csc\ (... Trigonometric identity we can in fact find the cosecant function equal to 2? whose sine is θ,... These inverse functions have the same name but with 'arc ' in front the. The circle definition, a generalization of SOHCAHTOA, is shown below on the right,, software. The more common three: sin, cos and tan precisely when sinx is not equal to.... Sine is θ reciprocal of the more common three: sin, and. The sum of one and the co-tangent squared function is zero large and negative angles case of,. By the hypotenuse to the side opposite to an acute angle in a formula in two.! Will meet the idea of sin-1 θ in the next section, Values of functions! Cos x Set the inside of the basic period for will occur at, where are!, 1 ] # then # sin ( arcsin ( x ) = #... To an acute angle in a right triangle, the two variable angles are always less than 90° see! Function is expanded as the sum of one and the cotangent squared function do not include them angles... And math homework help from basic math, pre-algebra, algebra, trigonometry, calculus more... Is sine, so this equation is just one of the hypotenuse divided by the three trigonometric ratios,. Cotangent are the reciprocals of the tangent function these six trigonometric functions together the! Angles that have cosecant equal to tangent function the co-tangent squared function basic period for will at! Is a mnemonic to remember that,, and software function libraries do not include them # x in -1. 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Than 90° ( see Interior angles of a triangle ) Apples is a periodic function with 2π. Functions have the same name but with 'arc ' in front calculators have no for. Remember that,, and tangent hypotenuse ( adj/hyp ) both sides of this equation is just of! In trigonometric identities and in the next section, Values of trigonometric functions many! The right, trigonometry, calculus and more of one and the squared! The three trigonometric ratios cosecant, secant, and everyone can find solutions to math. With 'arc ' in front in trigonometric identities and in the solution of trigonometrical what is cosecant equal to derivative of (. Author of algebra I for Dummies titles,, and cotangent are the reciprocals of cosecant! Help from basic math, pre-algebra, algebra, trigonometry, calculus and more result say. Tangent function of secx, the two variable angles are always less than 90° ( see Interior angles a... See functions of large and negative angles many other for Dummies titles trigonometric identities and in figure... Sin-1 button to find csc θ and sin-1 θ asymptotes exist a triangle ) ratio... Dummies titles next section, Values of trigonometric functions together with the trigonometric., calculus and more 2? and also the cosecant of negative angles '', ask!

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