12.3 Day 1 Notes Trigonometric Functions of General Angles Algebra 2 12.3 Day 1 Notes Trigonometric Functions of General Angles

Example 1A The terminal side of 𝜃 in standard position contains the point (8, −15). Find the exact values of the six trigonometric functions of 𝜃.

Example 1B – You try The terminal side of 𝜃 in standard position contains the point (−3, 4). Find the exact values of the six trigonometric functions of 𝜃.

Special Cases

Example 2A The terminal side of 𝜃 in standard position contains the point (0, −2). Find the exact values of the six trigonometric functions of 𝜃.

Example 2B – You try The terminal side of 𝜃 in standard position contains the point (3, 0). Find the exact values of the six trigonometric functions of 𝜃.

A reference angle is the acute angle formed by the terminal side of the angle and the x-axis.

Example 3 Sketch the angle 𝜃 and find the reference angle 𝜃 ′ for each angle 𝜃 given. a) 𝜃=140° b) 𝜃=−150°

Example 3 Continued Sketch the angle 𝜃 and find the reference angle 𝜃 ′ for each angle 𝜃 given. c) 𝜃= −5𝜋 6 d) 𝜃=320°

Exit Slip Part 1: The terminal side of 𝜃 in standard position contains the point (0, 5). Find the exact values of the six trigonometric functions of 𝜃. Part 2: Sketch the angle 𝜃 and find the reference angle 𝜃 ′ . 𝜃=145° 𝜃= 11𝜋 3