How do you express $cos (\frac{5 π}{4}) \cdot cos (\frac{2 π}{3})$ $cos( (5 pi)/4 ) * cos (( 2 pi) /3 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{5 π}{4}) \cdot cos (\frac{2 π}{3})$ $cos( (5 pi)/4 ) * cos (( 2 pi) /3 )$ without using products of trigonometric functions?

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Answer 1 · 2016-03-25T01:19:28

$\frac{\sqrt{2}}{4}$ $sqrt2/4$

Explanation:

$P = cos (\frac{5 π}{4}) . cos (\frac{2 π}{3})$ $P = cos ((5pi)/4) .cos ((2pi)/3)$
Trig unit circle and trig table give -->
$cos (\frac{5 π}{4}) = cos (\frac{π}{4} + π) = - cos (\frac{π}{4}) = - \frac{\sqrt{2}}{2}$ $cos ((5pi)/4) = cos (pi/4 + pi) = -cos (pi/4) = -sqrt2/2$
$cos (\frac{2 π}{3}) = cos (- \frac{π}{3} + π) = - \frac{cos π}{3} = - \frac{1}{2}$ $cos ((2pi)/3) = cos (-pi/3 + pi) = - cos pi/3 = - 1/2$
$P = (- \frac{\sqrt{2}}{2}) (- \frac{1}{2}) = \frac{\sqrt{2}}{4}$ $P = (-sqrt2/2)(-1/2) = sqrt2/4$

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How do you express $cos (\frac{5 π}{4}) \cdot cos (\frac{2 π}{3})$ $cos( (5 pi)/4 ) * cos (( 2 pi) /3 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{5 π}{4}) \cdot cos (\frac{2 π}{3})$ $cos( (5 pi)/4 ) * cos (( 2 pi) /3 )$ without using products of trigonometric functions?