How do you express $cos (\frac{5 π}{4}) \cdot cos (\frac{11 π}{6})$ $cos( (5 pi)/4 ) * cos (( 11 pi) /6 )$ without using products of trigonometric functions?

Question

How do you express $cos (\frac{5 π}{4}) \cdot cos (\frac{11 π}{6})$ $cos( (5 pi)/4 ) * cos (( 11 pi) /6 )$ without using products of trigonometric functions?

1 Answer

Impact of this question

1545 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-17T12:33:05

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

Explanation:

Product $P = cos (\frac{5 π}{4}) . cos (\frac{11 π}{4})$ $P = cos ((5pi)/4).cos ((11pi)/4)$
Trig table and unit circle -->
$cos (\frac{5 π}{4}) = cos (\frac{π}{4} + π) = - cos (\frac{π}{4}) = - \frac{\sqrt{2}}{2}$ $cos ((5pi)/4) = cos (pi/4 + pi) = - cos (pi/4) = - sqrt2/2$
$cos (\frac{11 π}{6}) = cos (- \frac{π}{6} + \frac{12 π}{6}) = cos (- \frac{π}{6} + 2 π) =$ $cos ((11pi)/6) = cos (-pi/6 + (12pi)/6) = cos (-pi/6 + 2pi) =$
$cos (- \frac{π}{6}) = cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}$ $cos (-pi/6) = cos (pi/6) = sqrt3/2$
Therefor:
$P = (- \frac{\sqrt{2}}{2}) (\frac{\sqrt{3}}{2}) = - \frac{\sqrt{6}}{4}$ $P = (-sqrt2/2)(sqrt3/2) = - sqrt6/4$

Science

Math

Humanities

... and beyond

How do you express $cos (\frac{5 π}{4}) \cdot cos (\frac{11 π}{6})$ $cos( (5 pi)/4 ) * cos (( 11 pi) /6 )$ without using products of trigonometric functions?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you express cos(5π4)⋅cos(11π6)cos( (5 pi)/4 ) * cos (( 11 pi) /6 ) without using products of trigonometric functions?

1 Answer

Explanation:

Related questions

Impact of this question

How do you express $cos (\frac{5 π}{4}) \cdot cos (\frac{11 π}{6})$ $cos( (5 pi)/4 ) * cos (( 11 pi) /6 )$ without using products of trigonometric functions?