4 Compound Angle Formula PDF

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Compound Angle Formulas

The compound angle formulas are: sin(𝛼 + 𝛽) = sin 𝛼 cos 𝛽 + cos 𝛼 sin 𝛽 sin(𝛼 − 𝛽) = sin 𝛼 cos 𝛽 − cos 𝛼 sin 𝛽 cos(𝛼 + 𝛽) = cos 𝛼 cos 𝛽 − sin 𝛼 sin 𝛽 cos(𝛼 − 𝛽) = cos 𝛼 cos 𝛽 + sin 𝛼 sin 𝛽 Examples: 1. Use the appropriate compound angle formula to express each of the following as a single trigonometric function, and then determine an exact value for each. 7𝜋 𝜋 2𝜋 7𝜋 2𝜋 𝜋 a. sin 3 cos 𝜋 + cos 3 sin 𝜋 b. cos 12 cos 4 + sin 12 sin 4

2. Use an appropriate compound angle formula to determine an exact value for each of the following. 𝜋 a. sin 15° b. cos (− 12)

Work: pg. 232 (1bc, 2ad, 3bd, 4a, 5b, 8, 9a, 10, 11d, 12, 13)

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Compound Angle Formulas c. cos

19𝜋

d. csc

12

4

5

3. Given that sin 𝛼 = 5 and sin 𝛽 = 13, where 0 < 𝛼 < cos(𝛼 + 𝛽).

Work: pg. 232 (1bc, 2ad, 3bd, 4a, 5b, 8, 9a, 10, 11d, 12, 13)

𝜋

2

5𝜋

12

𝜋

and < 𝛽 < 𝜋. Determine 2...