Use a sum or difference formula to find the exact value of the following. cos13π/15 cos7π/60 sin13π/15 sin7π/60.

Question

The answer cannot include sin or pie since the homework is not letting me use what I came up with... cos(13pi/60-7pi/60) = cos(6pi/60) = cos pi/10?

Answer 1

This is the subtraction angle identity of cosine with angles 13π/15 and 7π/60.

 

cos(13π/15 - 7π/60)

 

 

Using the LCD of the angles,

 

cos(52π/60 - 7π/60) =

 

cos(45π/60) =

 

cos(3π/4)

 

The angle 3π/4 is the angle π/4 rotated 3 times counterclockwise in a unit circle.  You will end up in the second quadrant. What is the value of cosine 45 degrees in the second quadrant?