How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{4 π}{3})$ $sin(pi/ 8 ) * cos(( ( 4 pi) / 3 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{4 π}{3})$ $sin(pi/ 8 ) * cos(( ( 4 pi) / 3 )$ without using products of trigonometric functions?

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Answer 1 · 2017-01-16T19:43:02

$(\frac{1}{2}) sin (\frac{π}{8})$ $(1/2)sin (pi/8)$

Explanation:

$P = sin (\frac{π}{8}) . \frac{cos (4 π)}{3}$ $P = sin (pi/8).cos (4pi)/3$
Trig table --> $\frac{cos (4 π)}{3} = cos (- \frac{π}{3} + π) = cos (- \frac{π}{3}) =$ $cos (4pi)/3 = cos (- pi/3 + pi) = cos (- pi/3) =$
$= cos (\frac{π}{3}) = \frac{1}{2}$ $= cos (pi/3) = 1/2$ . Then, P can be expressed as
$P = (\frac{1}{2}) sin (\frac{π}{8})$ $P = (1/2)sin (pi/8)$
We can evaluate $sin (\frac{π}{8})$ $sin (pi/8)$ by using the trig identity:
$2 {sin}^{2} (\frac{π}{8}) = 1 - cos (\frac{π}{4}) = 1 - \frac{\sqrt{2}}{2}$ $2sin^2 (pi/8) = 1 - cos (pi/4) = 1 - sqrt2/2$

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How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{4 π}{3})$ $sin(pi/ 8 ) * cos(( ( 4 pi) / 3 )$ without using products of trigonometric functions?

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Explanation:

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How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{4 π}{3})$ $sin(pi/ 8 ) * cos(( ( 4 pi) / 3 )$ without using products of trigonometric functions?