How do you express $sin (\frac{π}{4}) \cdot sin (\frac{9 π}{8})$ $sin(pi/ 4 ) * sin( ( 9 pi) / 8 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{9 π}{8})$ $sin(pi/ 4 ) * sin( ( 9 pi) / 8 )$ without using products of trigonometric functions?

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Answer 1 · 2016-04-24T23:13:25

$- \frac{\sqrt{2}}{2} sin (\frac{π}{8})$ $-sqrt2/2sin (pi/8)$

Explanation:

$P = sin (\frac{π}{4}) sin (\frac{9 π}{8})$ $P = sin (pi/4)sin ((9pi)/8)$
Trig table --> $sin (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ $sin (pi/4) = sqrt2/2$
sin ((9pi)/8) = sin (pi/8 + pi) = -sin (pi/8)
Therefor, the product P can be expressed as:
$P = - (\frac{\sqrt{2}}{2}) sin (\frac{π}{8})$ $P = -(sqrt2/2)sin (pi/8)$
Note.
We can find P, by evaluation $sin (\frac{π}{8})$ $sin (pi/8)$ , by using the trig identity:
$cos (\frac{π}{4}) = \frac{\sqrt{2}}{2} = 1 - 2 {sin}^{2} (\frac{π}{8})$ $cos (pi/4) = sqrt2/2 = 1 - 2sin^2 (pi/8)$

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{9 π}{8})$ $sin(pi/ 4 ) * sin( ( 9 pi) / 8 )$ without using products of trigonometric functions?

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Explanation:

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How do you express $sin (\frac{π}{4}) \cdot sin (\frac{9 π}{8})$ $sin(pi/ 4 ) * sin( ( 9 pi) / 8 )$ without using products of trigonometric functions?