# Answer to Question #9672 in Trigonometry for Eliana Hernandez

Question #9672

sin α = 4/5, α lies in quadrant II

cos β = 5/13, β lies in quadrant I

find the exact value of the following

1. cos (α + β)

2. tan (α - β)

3. sin 2α

4. cos β/2

verify each identity

9. cos (θ + (π/2)) = -sinθ

10. (sin (α - β))/(sin α cos β) = 1 - cot α tan β

11 sin t cos t(tan t + cot t) = 1

solve each equation on the interval [0,2π)

12. sin 3x = -1/2

13. sin 2x + cos x = 0

14. 2 sin^2 x + cos x = 1

15. 2 cos^2 x - 3 cos x +1 = 0

16. cos x = -0.092

17. tan x sec x = 3 tan x

18. tan^2 x - 3 tan x - 2 = 0

cos β = 5/13, β lies in quadrant I

find the exact value of the following

1. cos (α + β)

2. tan (α - β)

3. sin 2α

4. cos β/2

verify each identity

9. cos (θ + (π/2)) = -sinθ

10. (sin (α - β))/(sin α cos β) = 1 - cot α tan β

11 sin t cos t(tan t + cot t) = 1

solve each equation on the interval [0,2π)

12. sin 3x = -1/2

13. sin 2x + cos x = 0

14. 2 sin^2 x + cos x = 1

15. 2 cos^2 x - 3 cos x +1 = 0

16. cos x = -0.092

17. tan x sec x = 3 tan x

18. tan^2 x - 3 tan x - 2 = 0

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