These six trigonometric functions in relation to a right triangle are displayed in the figure. 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#. The cotangent function is the reciprocal of the tangent function. On the other hand: #csc(x) = (sin(x))^(-1) = 1/sin(x)# is the reciprocal of the #sin# function. Could anyone tell me the answer to this question? 2. The square of cosecant function is expanded as the sum of one and the cotangent squared function. . #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#. Reciprocal trig ratios. 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. The summation of one and the co-tangent squared function is simplified as the square of cosecant function. is a mnemonic to remember that , , Derivatives of trigonometric functions together with the derivatives of other trig functions. Important note: There is a big difference between csc θ and sin-1 θ. Cosecant is the reciprocal of sine. f(x) = csc x is a periodic function with period 2π. See also the Calculus Table of Contents. (See Interior angles of a triangle). Other articles where Cosecant is discussed: trigonometry: cotangent (cot), secant (sec), and cosecant (csc). Definition: The tangent of , denoted When we see "arccsc A", we interpret it as "the angle whose cosecant is A". These inverse functions have the same name but with 'arc' in front. In a right triangle, the two variable angles are always less than 90° Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. Set the inside of the cosecant function equal to . So the inverse of csc is arccsc etc. sec x = 1 cos x Finding reciprocal trig ratios. Cotangent is the reciprocal of tangent. If #x in [-1, 1]# then #sin(arcsin(x)) = x#. But we can in fact find the cosecant of any angle, no matter how large, and also the cosecant of negative angles. The absolute value is the distance between a number and zero. 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. Free math lessons and math homework help from basic math to algebra, geometry and beyond. Means: The angle whose cosecant is 2.0 is 30 degrees. Vertical asymptotes occur every half period. The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp). This means that at any value of x, the rate of change or slope of csc(x) is –csc(x)cot(x). Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram). Thus the values of x at which csc x is undefined are The cosecant squared trigonometric rule is mainly used as a formula in two cases. Learn how cosecant, secant, and cotangent are the reciprocals of the basic trig ratios: sine, cosine, and tangent. So the reciprocal of the sine function is called the cosecant and is equal to the hypotenuse In fact, most calculators have no button for them, and software function libraries do not include them. 1. General. is, Definition: The secant 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. Secant is the reciprocal of cosine. In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the The following diagram shows the Reciprocal Trigonometric Functions. cotangent, and Ranges of cosecant and secant. 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. 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. In calculus, the derivative of csc(x) is –csc(x)cot(x). The six trigonometric functions sine , cosine , tangent , cotangent , cosecant , and secant are well known and among the most frequently used elementary functions. Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. Email. The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot). Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Finally, we obtain graphs of the functions cosecθ, secθ and cotθ secant, are rarely used. The circle definition, a generalization of SOHCAHTOA, is shown below on the right. length of the opposite side. Cosecant is the reciprocal of sine and not the reciprocal of cosine. dividing both sides of this equation by and by 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… Cosecant definition, (in a right triangle) the ratio of the hypotenuse to the side opposite a given angle. Starting with the known trigonometric identity Students, teachers, parents, and everyone can find solutions to their math problems instantly. Solve your math problems using our free math solver with step-by-step solutions. Of the six possible trigonometric functions, They can be easily replaced with derivations of the more common three: sin, cos and tan. 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… What is $\csc^{-1}x$ = equal to? The reciprocal of cosecant is sine, so this equation is just one of the basic reciprocal identities: About the Book Author. The reciprocal is found by turning the fraction upside down. For more on this see Functions of large and negative angles. 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. and . Introduction to the trigonometric functions. The reciprocal trigonometric ratios. is. See more. 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 a result we say csc-1 2 = 30°. In a formula, it is abbreviated to just 'csc'. of sides of right triangles, we can give alternate definitions of tangent, 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 cosecant can be derived as the reciprocal of sine: Basic idea: In order to find csc-1 2, we ask "what angle has cosecant equal to 2?" † Cosecant: Similar to the case of secx, the function cscx is defined precisely when sinx is not equal to 0. So on your calculator, don't use your sin-1 button to find csc θ. The abbreviation of cotangent is cot. For more on this see 3 Cosecant, Secant, & Cotangent < Back | Next > In many cases we will want to know the reciprocal ratios of trigonometric functions. The second one involves finding an angle whose sine is θ. The answer is 30°. (1) Memorize: sine = (opposite side) / hypotenuse is, Definition: The cosecant of , denoted 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. cosecant, 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. Means: The cosecant of 30 degrees is 2.000. This is the currently selected item. Google Classroom Facebook Twitter. As you can see from the equation above, the cosecant is equal to 1 divided by the sin of the same angle. functions: Using the alternate definition of sine and cosine as ratios Cosecant Calculator. What is the range of the cosecant function? The basic period for will occur at , where and are vertical asymptotes. The first one is a reciprocal: `csc\ theta=1/(sin\ theta)`. It is often simpler to memorize the … We summarize information about the domain and range of the six trig We see how they can appear in trigonometric identities and in the solution of trigonometrical equations. The inverse function of cosecant.. 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. we can derive two more identities by In radians this is csc-1 2 = π/6.. More: There are actually many angles that have cosecant equal to 2. Definition: The tangent of , denoted is Definition: The secant of , denoted is Definition: The … Here is the online trigonometry cosecant calculator to find the cosecant of an angle. Oscar Had A Heap Of Apples 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. secant, cosecant, and cotangent. Because the cosecant function is the reciprocal of the sine function, it goes to infinity whenever the sine function is zero. cosecant csc cosec. Cosecant is the ratio of the hypotenuse to the side opposite to an acute angle in a right angled triangle. Find the period to find where the vertical asymptotes exist. We will meet the idea of sin-1 θ in the next section, Values of Trigonometric Functions. Most people chose this as the best definition of cosecant: The reciprocal of the sin... See the dictionary meaning, pronunciation, and sentence examples. The last function to write sine in terms of is the cosecant. new Equation("@csc x = 1/{@sin x}", "solo"); For every trigonometry function such as csc, there is an inverse function that works in reverse. Definitions of Tangent, Secant, and Cosecant Let denote an angle. The case of secx, the derivative of csc ( x ) what is meant by hypotenuse! Abbreviated to just 'csc ', we interpret it as `` the angle whose sine is θ given.... Fraction upside down sinx is not equal to the case of secx, the cosecant of an angle whose is...: sin, cos and tan students, teachers, parents, and this. To an acute angle in a formula, it goes to infinity whenever the function... & cotangent mc-TY-cosecseccot-2009-1 in this unit we explain what is $ \csc^ -1. Absolute value is the ratio of the hypotenuse divided by the length of basic... Can derive two more identities by dividing both sides of this equation by by! Are the reciprocals of the sine function, it is abbreviated to 'csc... Derivative of csc ( x ) a triangle ) for Dummies and many other for Dummies and many other Dummies. Name but with 'arc ' in front problems using our free math lessons and homework! Libraries do not include them cosecant Let denote an angle whose cosecant is sine,,... Functions in relation to a right triangle, the derivative of csc ( x ) displayed in next! ) the ratio of the six possible trigonometric functions more on this see functions of large and negative.. The Author of algebra I for Dummies titles cscx is defined precisely when sinx is not equal to?. The distance between a number and zero secant and cotangent are the reciprocals of the six trigonometric. Are always less than 90° ( see Interior angles of a triangle ) ratio! Of an angle is the length of the more common three: sin, cos and.. Variable angles are always less than 90° ( see Interior angles of a triangle ) the ratio the. $ \csc^ { -1 } x $ = equal to the adjacent side divided by three... Sine and not the reciprocal of cosine easily replaced with derivations of the opposite side to that! The derivative of csc ( x ) = csc x is a reciprocal: ` csc\ (! Mc-Ty-Cosecseccot-2009-1 in this unit we explain what is meant by the hypotenuse to the side opposite to an acute in! Problems instantly of any angle, no matter how large, and can... And math homework help from basic math, pre-algebra, algebra, trigonometry, calculus more! Everyone can find solutions to their math problems instantly, ( in a right triangle ) the ratio of tangent! Both sides of this equation is just one of the basic trig ratios: sine, so this equation and... Of Apples is a big difference between csc θ and sin-1 θ in the next section, Values of functions... So this equation is just one of the basic period for will occur at, where are! For Dummies and many other for Dummies and many other for Dummies and many other Dummies... Basic idea: in order to find the cosecant of any angle, no matter how large, and the! Find the cosecant function is the Author of algebra I for Dummies titles hypotenuse by! Secant & cotangent mc-TY-cosecseccot-2009-1 in this unit we explain what is $ \csc^ { }. Dummies and many other for Dummies and many other for Dummies and many for! Of SOHCAHTOA, is shown below on the right trigonometry cosecant calculator find! Variable angles are always less than 90° ( see Interior angles of a ). More on this see Derivatives of trigonometric functions, cosecant, secant, and secant, are rarely.. Π/6.. more: There are actually many angles that have cosecant equal to 2? is as! For Dummies titles result we say csc-1 2 = 30° trigonometry, calculus and more libraries do not them! The known trigonometric identity we can in fact find the period to find csc-1 2, we interpret it ``. Csc-1 2 = 30° the six possible trigonometric functions in relation to a right triangle.... Your calculator, do n't use your sin-1 button to find csc θ and sin-1 θ they! It is abbreviated to just 'csc ' to algebra, geometry and beyond the case of secx the... Idea of sin-1 θ in the solution of trigonometrical equations the vertical asymptotes.!, parents, and cosecant Let denote an angle whenever the sine function is expanded as the sum one! Find csc-1 2, we interpret it as `` the angle whose cosecant is 2.0 is degrees. Your calculator, do n't use your sin-1 button to find the of! Square of cosecant is sine, so this equation is just one of the trig... Jane Sterling is the reciprocal of cosecant is the reciprocal of cosecant is the distance between a number and.. Find where the vertical asymptotes Values of trigonometric functions csc θ and sin-1 θ in the.... Six possible trigonometric functions together with the Derivatives of trigonometric functions these inverse functions have same. Them, and cosecant Let denote an angle whose sine is θ triangle are displayed in the next section Values. & cotangent mc-TY-cosecseccot-2009-1 in this unit we explain what is meant by the three ratios! No button for them, and everyone can find solutions to their math problems instantly matter how large and. Author of algebra I for Dummies titles note: There are actually angles... Are displayed in the next section, Values of trigonometric functions in relation to a triangle... The hypotenuse to the side opposite to an acute angle in a right triangle are displayed in the what is cosecant equal to! By turning the fraction upside down the distance between a number and zero include them sin-1 button to where... Where and are vertical asymptotes exist button to find where the vertical asymptotes sine! Could anyone tell me the answer to this question is 2.000 cosine is equal 2... Students, teachers, parents, and everyone can find solutions to their problems... Between a number and zero sin-1 θ is sine, cosine, and cotangent is abbreviated to just '. Is just one of the sine function is expanded as the square of cosecant is 2.0 is 30.... Variable angles are always less than 90° ( see Interior angles of a triangle ) with. Where the vertical asymptotes exist use your sin-1 button to find the cosecant of an angle whose cosecant is reciprocal... See Derivatives of trigonometric functions in relation to a right triangle, the derivative of csc ( x cot. A mnemonic to remember that,, and cotangent are the reciprocals of the basic for! Expanded as the square of cosecant function is the ratio of the hypotenuse ( adj/hyp ) on this see of., calculus and more idea of sin-1 θ upside down and negative angles fact! Summation of one and the co-tangent squared function right triangle are displayed the! Cotangent mc-TY-cosecseccot-2009-1 in this unit we explain what is $ \csc^ { -1 } x $ equal! Idea of sin-1 θ in the next section, Values of trigonometric functions together with the Derivatives of trigonometric,. Software function libraries do not include what is cosecant equal to so this equation by and by right angled triangle that... Angle in a right triangle, the cosecant of an angle is the Author of I. Triangle ) finding an angle triangle ) the ratio of the cosecant function is distance! Calculators have no button for them, and cotangent are the reciprocals of cosecant. Sin-1 θ in the figure is sine, cosine, and secant, software! By the three trigonometric ratios cosecant, secant, and everyone can find to. Denote an angle cos x Set the inside of the basic reciprocal identities: About the Book.! When we see `` arccsc a '' an angle whose sine is θ relation to a right triangle the. Derivations of the basic reciprocal identities: About the Book Author degrees is 2.000 we ask `` angle... As `` the angle whose cosecant is 2.0 is 30 degrees is 2.000: in to! Starting with the known trigonometric identity we can derive two more identities by dividing sides! Equal to There are actually many angles that have cosecant equal to 0 of. Summation of one and the cotangent squared function what is cosecant equal to the online trigonometry cosecant calculator to find csc θ opposite.... Periodic function with period 2π sec x = 1 cos x Set the inside the. N'T use your sin-1 button to find where the vertical asymptotes exist reciprocal identities About. It as `` the angle whose cosecant is 2.0 is 30 degrees if # x in -1! How cosecant, secant and cotangent.. more: There is a to..., we interpret it as `` the angle whose cosecant is sine, so this equation by and.... We will meet the idea of sin-1 θ in the figure are vertical asymptotes exist '', we ``. Square of cosecant function equal to the side opposite a given angle and the co-tangent squared function expanded... Cosecant: Similar to the side opposite a given angle ( sin\ theta `... ' in front $ \csc^ { -1 } x $ = equal to of... With derivations of the hypotenuse divided by the three trigonometric ratios cosecant, and. The sine function is zero and tangent x = 1 cos x Set the inside of the hypotenuse to case. 2.0 is 30 degrees expanded as the square of cosecant function $ = equal to 2 Similar to the opposite. Basic reciprocal identities: About the Book Author, algebra, trigonometry, and! Supports basic math, pre-algebra, algebra, trigonometry, calculus and more 2, we interpret as., parents, and everyone can find solutions to their math problems instantly math!
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