What is the input for inverse trigonometric functions

An inverse trigonometric function is a function in which you can input a number and get/output an angle (usually in radians). It is the inverse function of the basic trigonometric functions.

Step-by-step explanation:

Trigonometric functions are derived from ratios of certain sides of a right triangle in reference to an angle. The graph of which is a wave, with amplitude in the y-axis and angle in the x-axis. We will first define the sine function written as:

sin (θ) = oppositesidehypotenuse

As we can see, the sine function, together with all the other trigonometric functions, relates an angle to the ratio of an opposite side and the hypotenuse of right triangle. The input here is an angle, and the output is a ratio. Therefore, the inverse process to this is actually just a reverse process.

Let

y

=

s

i

n

(

θ

)

y=sin (θ)

Then inverse trigonometric function outputs an angle. However, we can set y to its original value via transitivity:

s

i

n

-

1

(

y

)

=

θ

s

i

n

-

1

(

o

p

p

o

s

i

t

e

s

i

d

e

h

y

p

o

t

e

n

u

s

e

)

=

θ

sin-1 (y) = θsin-1 (oppositesidehypotenuse) = θ

Thus we see, that the input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.