Question

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Write sinπ/5cosπ/8+cosπ/5sinπ/8 as a trigonometric function of one number. Keep π in your answer. Be sure to PREVIEW your answer before submitting!

Answer 1

sin(13π/40)

Explanation:

The given expression matches the pattern ...

sin(a)cos(b) +cos(a)sin(b) = sin(a+b)

Then ...

sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)

= sin(13π/40)

_____

π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)