Download Inverse Trigonometric Functions

4.7A
Inverse Trigonometric Functions
 Inverse Trigonometric Functions allow you to find an
angle if you are given its trig ratio.
 To access inverse trig function on the calculator, press
the 2nd key, and then the associated trig function. Be
sure to check if the calculator is in Radian Mode or
Degree Mode.
 sin−1 𝑥 = θ
cos −1 𝑥 = 𝜃
tan−1 𝑥 = 𝜃
Inverse Sine Function
 also known as Arcsine Function and written sin−1 𝑥 or arcsin x
 Domain: [-1, 1]
Range: [
−𝜋 𝜋
, ]
2 2
1
2
 Ex. Given that the sin ratio of an angle is , find the angle with and
without a calculator.
1
2
𝜋
6
sin−1 ( ) = = 30o
Using the unit circle:
1
2
Find the angle that has a sine of .
Remember, sine is the y-coordinate in the pairs.
Inverse Cosine Function
 also known as Arccosine Function and written as cos-1 or arcos x
 Domain: [-1, 1]
Range: [0, 𝜋]
1
2
 Ex. Given that the cos ratio of an angle is , find the angle with
and without a calculator.
−1 1
cos ( )
2
𝜋
3
= = 60o
Using the unit circle:
Find the angle that has a cos of
1
.
2
Remember, cosine is the x-coordinate in the pairs.