5.2 Sum and Difference Formulas Objectives: Use the sum and difference formulas for sine, cosine and tangent.

DO NOW A pendulum 4 feet long travels 10 feet in one direction each swing. What is the angle measure of the swing, as measured in radians? 2.5 In standard position, an angle of − 𝜋 3 radians has the same terminal angle as what degree measure? 300o

Sum and Difference Formulas for Cosines, Sine, and Tangent

Sum and Difference Formulas for Cosines, Sine, and Tangent Use the angle sum identity to find the exact value of each.

Sum and Difference Formulas for Cosines, Sine, and Tangent Use the angle sum identity to find the exact value of each.

Sum and Difference Formulas for Cosines, Sine, and Tangent Use the angle sum identity to find the exact value of each.

Speed Quiz #6- February 27th 5.2 Sum and Difference Formulas Objectives: Use the sum and difference formulas for sine, cosine and tangent. Assignment: pg. 603 #’s 9, 11, 33-43 odd, 57-63 odd Speed Quiz #6- February 27th

DO NOW In the figure below, if sin 𝑛 𝑜 + sin 𝑛 𝑜 =1 , then 𝑥 𝑜 = A) 90 B) 60 C) 45 D) 30 In the figure below, sinB – sinA = 1/8 B) ½ C) 5/8 D) 2/3

Example: Verifying an Identity Verify the identity: cos ( 𝛼−𝛽) cos 𝛼 cos 𝛽 = cos 𝛼 cos 𝛽 + sin 𝛼 sin 𝛽 cos 𝛼 cos 𝛽 Divide by cos α cos β. The identity is verified.

Example: Verifying an Identity Verify the identity: The identity is verified.

Example: Finding Exact Values Suppose that for a quadrant II angle and for a quadrant I angle Find the exact value of 𝛼

Example: Finding Exact Values Suppose that for a quadrant II angle and for a quadrant I angle Find the exact value of 𝛽 𝛽

Example: Finding Exact Values Suppose that for a quadrant II angle and for a quadrant I angle Find the exact value of

Verify the Identity

61.

61.

57.

59.

63.