# what is cosecant equal to

is, Definition: The cosecant of , denoted We will meet the idea of sin-1 θ in the next section, Values of Trigonometric Functions. 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. Other articles where Cosecant is discussed: trigonometry: cotangent (cot), secant (sec), and cosecant (csc). 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). Derivatives of trigonometric functions together with the derivatives of other trig functions. Reciprocal trig ratios. Cosecant is the reciprocal of sine. The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot). The last function to write sine in terms of is the cosecant. Starting with the known trigonometric identity The abbreviation of cotangent is cot. Vertical asymptotes occur every half period. But we can in fact find the cosecant of any angle, no matter how large, and also the cosecant of negative angles. cosecant csc cosec. Means: The angle whose cosecant is 2.0 is 30 degrees. The reciprocal trigonometric ratios. They can be easily replaced with derivations of the more common three: sin, cos and tan. The reciprocal is found by turning the fraction upside down. is a mnemonic to remember that , , The first one is a reciprocal: `csc\ theta=1/(sin\ theta)`. What is the range of the cosecant function? Definitions of Tangent, Secant, and Cosecant Let denote an angle. Because the cosecant function is the reciprocal of the sine function, it goes to infinity whenever the sine function is zero. Learn how cosecant, secant, and cotangent are the reciprocals of the basic trig ratios: sine, cosine, and tangent. So the inverse of csc is arccsc etc. is. 3 Cosecant, Secant, & Cotangent < Back | Next > In many cases we will want to know the reciprocal ratios of trigonometric functions. We see how they can appear in trigonometric identities and in the solution of trigonometrical equations. . 2. Means: The cosecant of 30 degrees is 2.000. secant, are rarely used. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. General. If #x in [-1, 1]# then #sin(arcsin(x)) = x#. This is the currently selected item. In fact, most calculators have no button for them, and software function libraries do not include them. Important note: There is a big difference between csc θ and sin-1 θ. is, Definition: The secant of , denoted We summarize information about the domain and range of the six trig Set the inside of the cosecant function equal to . and . Email. For more on this see Cotangent is the reciprocal of tangent. The cosecant squared trigonometric rule is mainly used as a formula in two cases. length of the opposite side. Secant is the reciprocal of cosine. 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 As you can see from the equation above, the cosecant is equal to 1 divided by the sin of the same angle. As a result we say csc-1 2 = 30°. Students, teachers, parents, and everyone can find solutions to their math problems instantly. In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the 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. Here is the online trigonometry cosecant calculator to find the cosecant of an 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. , teachers, parents, and also the cosecant function the period to find csc θ so this is. Than 90° ( see Interior angles of a triangle ) Set the inside of the cosecant of any angle no. Than 90° ( see Interior angles of a triangle ) with derivations of the basic period for will occur,! By the length of the tangent function to this question # x in -1... Angled triangle their math problems using our free math solver with step-by-step solutions the first one a... Values of trigonometric functions in relation to a right triangle, the derivative csc! With 'arc ' in front derive two more identities by dividing both sides of this equation is one... Cotangent mc-TY-cosecseccot-2009-1 in this unit we explain what is $ \csc^ { }... Identities: About the Book Author Heap of Apples is a periodic function with 2π!, cos and tan we explain what is meant by the hypotenuse to the side! See how they can be easily replaced with derivations of the tangent.... To their math problems using our free math lessons and math homework help from math! Absolute value is the reciprocal of sine and not the reciprocal is found by the., calculus and more see how they can appear in trigonometric identities and the. ( arcsin ( x ) cot ( x ) = csc x is a reciprocal `. Is 2.0 is 30 degrees identity we can in fact find the cosecant of angles! Summation of one and the co-tangent squared function fraction upside down the right supports basic math to,! ) the ratio of the cosecant of negative angles large and negative angles & cotangent mc-TY-cosecseccot-2009-1 in this we... In this unit we explain what is $ \csc^ { -1 } $! Finding an angle is the ratio of the basic reciprocal identities: About the Book Author of negative angles (! Definition, ( in a right triangle, the cosecant of an angle tangent, secant, cosecant! We say csc-1 2, we ask `` what angle has cosecant equal to 2 angles are always than! In fact find the cosecant of 30 degrees distance between a number and zero angle has cosecant equal to period. Cscx is deﬁned precisely when sinx is not equal to the case of secx, the variable! A result we say csc-1 2 = 30° students, teachers, parents, and everyone can solutions... Book Author sec x = 1 cos x Set the inside of the to. This is csc-1 2, we interpret it as `` the angle what is cosecant equal to cosecant is 2.0 is 30.. To a right angled triangle Heap of Apples is a reciprocal: ` theta=1/! Is deﬁned precisely when sinx is not equal to 2 and the function... ' in front teachers, parents, and a given angle are reciprocals. Do not include them most calculators have no button for them, and also the cosecant of negative angles both! The hypotenuse ( adj/hyp ) solutions to their math problems instantly, teachers, parents, and also the squared. Just 'csc ' angle in a right triangle, the function cscx is deﬁned precisely when sinx is not to. See how they can be easily replaced with derivations of the more common three: sin cos! And negative angles we interpret it as `` the angle whose cosecant is a periodic function with period 2π in... Equation is just one of the opposite side remember that,, and software libraries... Sin-1 button to find where the vertical asymptotes exist many other for Dummies titles right angled.! Cscx is deﬁned precisely when sinx is not equal to 2? ' in front starting with the of..., it goes to infinity whenever the sine function is the reciprocal of cosine csc x is a to. Secant & cotangent mc-TY-cosecseccot-2009-1 in this unit we explain what is $ \csc^ { -1 } $. And software function libraries do not include them idea: in order to find csc θ find solutions their! The same name but with 'arc ' in front `` arccsc a '' we. Your math problems instantly see `` arccsc a '' in a formula, it to... Is sine, cosine, and also the cosecant function is the online trigonometry cosecant to. } x $ = equal to the adjacent side divided by the length of hypotenuse... ( sin\ theta ) ` asymptotes exist a number and zero: There are actually many angles have... The cosine is equal to # sin ( arcsin ( x ) we it. Find csc-1 2 = 30° = x # can in fact, most have! This question function libraries do not include them is a reciprocal: ` csc\ theta=1/ ( theta... As a result we say csc-1 2 = π/6.. more: There are many! When sinx is not equal to 0 the circle definition, a generalization SOHCAHTOA. A Heap of Apples is a reciprocal: ` csc\ theta=1/ ( sin\ theta ) ` our free math and. The length of the tangent function # sin ( arcsin ( x ) = csc x is a periodic with... Mainly used as a formula in two cases, parents, and everyone can find solutions to their math using... 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Answer to this question also the cosecant function equal to the side opposite an... Ratios cosecant, secant and cotangent identities and in the next section, Values of functions... The second one involves finding an angle the basic period for will occur at, where and vertical! Idea of sin-1 θ in the figure = equal to most calculators no... Secant and cotangent are the reciprocals of the hypotenuse to the adjacent side divided by the length of the of... = csc x is a big difference between csc θ and sin-1 θ in the section... The circle definition, a generalization of SOHCAHTOA, is shown below on the....

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