Section 7-6 The Inverse Trigonometric Functions

Inverse Trig. Functions With the trigonometric functions, we start with an angle, θ, and use one or more of the functions to find a value. With the inverse trigonometric functions, we start with a value and try to find the angle.

Inverse Trig. Functions sin -1 xdomain: -90º ≤ x ≤ 90º (first and fourth quadrants) cos -1 xdomain: 0º ≤ x ≤ 180º (first and second quadrants) tan -1 xdomain: -90º ≤ x ≤ 90º (first and fourth quadrants)

Using the Unit Circle Example 1: Use your unit circle diagram to find the following (in degrees): a) cos -1 (-1)b) sin -1 0 c) sin -1 d) sin -1 (1) e) cos -1 f) cos -1

Using a Calculator Above the sin, cos, and tan buttons on the calculator, you will see sin -1, cos -1, tan -1. To use these inverse functions, we must enter the value, hit the second or shift button, then the correct function.

Using a Calculator Example 2: Use a calculator to find the following in degrees: a) tan -1 b) tan -1 1 c) tan -1 (-1)

Using a calculator Example 3: Use a calculator to find the following (in deg.) a) tan -1 (1.2) b) sin -1 (-0.3) c) cos -1 (-0.425)

Using a Calculator Example 4: Use a calculator to find the following (in radians). a) tan -1 (-2.9) b) sin -1 (0.75) c) cos -1 (0.058)

Example 5: Find Answer: or 0.6

Example 6: Find Answer: or 1.202

Example 7: Find Answer: 0

HOMEWORK pg. 289; 2 – 8 even pg. 290; 12, 14