How do you express $sin (\frac{π}{12}) \cdot cos (\frac{19 π}{12})$ $sin(pi/12) * cos(( 19 pi)/12 )$ without products of trigonometric functions?

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{19 π}{12})$ $sin(pi/12) * cos(( 19 pi)/12 )$ without products of trigonometric functions?

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Answer 1 · 2016-03-25T01:01:33

sin^2 (pi/12)

Explanation:

The trig unit circle and the property of complementary arcs give -->
$cos (\frac{19 π}{12}) = cos (\frac{7 π}{12} + π) = - cos (\frac{7 π}{12}) =$ $cos ((19pi)/12) = cos ((7pi)/12 + pi) = -cos ((7pi)/12) =$
$= - cos (\frac{π}{12} + \frac{π}{2}) = sin (\frac{π}{12})$ $= - cos (pi/12 + pi/2) = sin (pi/12)$
Reminder: $cos (a + \frac{π}{2}) = - sin a$ $cos (a + pi/2) = - sin a$

Finally, the product can be expressed as:
$P = {sin}^{2} (\frac{π}{12})$ $P = sin^2 (pi/12)$

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{19 π}{12})$ $sin(pi/12) * cos(( 19 pi)/12 )$ without products of trigonometric functions?

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How do you express sin(pi/12) * cos(( 19 pi)/12 ) sin(π12)⋅cos(19π12)sin(pi/12) * cos(( 19 pi)/12 ) without products of trigonometric functions?

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How do you express $sin (\frac{π}{12}) \cdot cos (\frac{19 π}{12})$ $sin(pi/12) * cos(( 19 pi)/12 )$ without products of trigonometric functions?