Question

How do you express `cos( (15 pi)/ 8 ) * cos (( 4 pi) /3 )` without using products of trigonometric functions?

Answer 1

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

Explanation:

Use trig table of special arcs and unit circle -->
`cos ((15pi)/8) = cos ((16pi)/8 - pi/8) = cos (2pi - pi/8) = cos - pi/8 = cos (pi/8)`
`cos ((4pi)/3) = cos (pi/3 + pi) = - cos (pi/3) = - 1/2`
`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)