How do you express $sin (\frac{π}{8}) \cdot cos (\frac{5 π}{8})$ $sin(pi/ 8 ) * cos(( 5 pi)/8 )$ without products of trigonometric functions?

Question

How do you express $sin (\frac{π}{8}) \cdot cos (\frac{5 π}{8})$ $sin(pi/ 8 ) * cos(( 5 pi)/8 )$ without products of trigonometric functions?

1 Answer

Impact of this question

1987 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-25T12:09:01

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

Explanation:

Trig unit circle and the property of complementary arcs give -->
$cos (\frac{5 π}{8}) = cos (\frac{π}{8} + \frac{4 π}{8}) = cos (\frac{π}{8} + \frac{π}{2}) = - sin (\frac{π}{8})$ $cos ((5pi)/8) = cos (pi/8 + (4pi)/8) = cos (pi/8 + pi/2) = - sin (pi/8)$
Therefor, the product can be expressed as:
$P = sin (\frac{π}{8}) . cos (\frac{5 π}{8}) = - {sin}^{2} (\frac{π}{8})$ $P = sin (pi/8).cos ((5pi)/8) = - sin^2 (pi/8)$

Science

Math

Humanities

... and beyond

How do you express $sin (\frac{π}{8}) \cdot cos (\frac{5 π}{8})$ $sin(pi/ 8 ) * cos(( 5 pi)/8 )$ without products of trigonometric functions?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you express sin(pi/ 8 ) * cos(( 5 pi)/8 ) sin(π8)⋅cos(5π8)sin(pi/ 8 ) * cos(( 5 pi)/8 ) without products of trigonometric functions?

1 Answer

Explanation:

Related questions

Impact of this question

How do you express $sin (\frac{π}{8}) \cdot cos (\frac{5 π}{8})$ $sin(pi/ 8 ) * cos(( 5 pi)/8 )$ without products of trigonometric functions?