Problem of the Day The figure at the right represents a unit circle. Which statement BEST represents the relationships between angles q and r? The angles are equal. The angles have equal sines. The angles have equal cosines. The angles are opposite of each other. Problem of the Day

Section 12-6 & 13-1 Trigonometric Expressions and Identities

Then Now Objectives You found values of trigonometric functions based on the unit circle. You used the properties of periodic functions to evaluate trigonometric functions. Use trigonometric identities to find trigonometric values.

Common Core State Standards Content Standards F.TF.1 – Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. F.TF.2 – Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Mathematical Practices 7) Look for and make use of structure. Common Core State Standards

The exact values of the cos θ and sin θ for special angles are shown on the unit circle below. The cosine values are the x-coordinates of the points on the unit circle and the sine values are the y-coordinates.

Find the exact value of the expression: cos (− 5𝜋 6 ) Example 4 (12-6)

Find the exact value of the expression: sin 495° Example 4 (12-6)

Find the exact value of the expression: cos ( 11𝜋 4 ) sin -600° Example 4 (12-6)

Find sin θ if cos θ = 1 3 and 270° < θ < 360°. Example 1 (13-1)

Find sec θ if sin θ = − 2 7 and 180° < θ < 270°. Example 1 (13-1)

Find csc θ if cos θ = 5 13 and 0° < θ < 90°. Example 1 (13-1)

p.833 #7, 21, 23, 25 and p.876 #9, 11, 13, 16, 19, 20 Homework