How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{4 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 4 pi) /3 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{4 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 4 pi) /3 )$ without using products of trigonometric functions?

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Answer 1 · 2016-09-18T18:26:30

-(1/2)cos (pi/8)

Explanation:

Use trig table of special arcs and unit circle -->
$cos (\frac{15 π}{8}) = cos (\frac{16 π}{8} - \frac{π}{8}) = cos (2 π - \frac{π}{8}) = cos - \frac{π}{8} = cos (\frac{π}{8})$ $cos ((15pi)/8) = cos ((16pi)/8 - pi/8) = cos (2pi - pi/8) = cos - pi/8 = cos (pi/8)$
$cos (\frac{4 π}{3}) = cos (\frac{π}{3} + π) = - cos (\frac{π}{3}) = - \frac{1}{2}$ $cos ((4pi)/3) = cos (pi/3 + pi) = - cos (pi/3) = - 1/2$
$cos (\frac{15 π}{8}) = cos (- \frac{π}{8} + 2 π) = cos (- \frac{π}{8}) = cos (\frac{π}{8})$ $cos ((15pi)/8) = cos (-pi/8 + 2pi) = cos (-pi/8) = cos (pi/8)$
The product can be expressed as:
P = -(1/2)cos (pi/8)

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{4 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 4 pi) /3 )$ without using products of trigonometric functions?

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How do you express $cos (\frac{15 π}{8}) \cdot cos (\frac{4 π}{3})$ $cos( (15 pi)/ 8 ) * cos (( 4 pi) /3 )$ without using products of trigonometric functions?