4.3 – Trig Functions on the Unit Circle Objective: You should be able to find the values of trig functions for any angle.

Example 1: Let (–4, 3) be a point on the terminal side of an angle θ in standard position. Find the exact values of the six trigonometric functions of θ.

Example 2: Find the exact value. If not defined, write undefined. a. cos π b. tan 450° c. 𝒄𝒐𝒕 𝟕𝝅 𝟐

Example 3: Sketch the angle. Then find its reference angle. –150° b. 𝟑𝝅 𝟒 c. 520º

“All Students Take Calculus”

Example 4: Find the exact value of: 𝒔𝒊𝒏 𝟒𝝅 𝟑 b. tan 150º c. 𝒔𝒆𝒄 𝟏𝟓𝝅 𝟒

Example 5: Let csc 𝜽 = –3, tan 𝜽 < 0. Find the exact values of the remaining five trigonometric functions of 𝜽.

Example 6: A student programmed a 10-inch long robotic arm to pick up an object at point C and rotate through an angle of 150° in order to release it into a container at point D. Find the position of the object at point D, relative to the pivot point O.

Example 7: Find the exact value. If not defined, write undefined. a. 𝒔𝒊𝒏 𝟕𝝅 𝟔 b. 𝐭𝐚𝐧 𝟒𝝅 𝟑 c. 𝒔𝒆𝒄 𝟐𝟕𝟎º

Example 8: Find the exact value of all 6 trig functions for 𝜽= 𝟓𝝅 𝟔 .

Example 9: Find the exact value of 𝒄𝒐𝒔 𝟗𝝅 𝟒 . 𝒔𝒊𝒏 (−𝟑𝟎𝟎)° 𝒕𝒂𝒏 𝟐𝟗𝝅 𝟔