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

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

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Answer 1 · 2018-03-13T23:28:25

$- \frac{\sqrt{6}}{4}$ $-sqrt6/4$

Explanation:

$P = sin (\frac{π}{4}) . sin (\frac{4 π}{3})$ $P = sin (pi/4).sin ((4pi)/3)$ =
Trig table and unit circle gives -->
$sin (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ $sin(pi/4) = sqrt2/2$ , and $sin (\frac{4 π}{3}) = - sin (\frac{π}{3}) = - \frac{\sqrt{3}}{2}$ $sin ((4pi)/3) = - sin (pi/3) = - sqrt3/2$
Therefor -->
$P = (\frac{\sqrt{2}}{2}) (- \frac{\sqrt{3}}{2}) = - \frac{\sqrt{6}}{4}$ $P = (sqrt2/2)(- sqrt3/2) = - sqrt6/4$

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

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