Here's the question(s)


1. Find the exact value of cos (13 pi-radian) / 12

2. If x is between intervals (pi/2, pi), and y is in the interval (pi, 3pi/2)
cos(x) = -5/13
tan(y) = 4/3

evaluate cos(x+y)

I know you have to use multiple subtractions for the second, but i don't know anymore....

13pi can be reduced every 2pi

in other words, 13 pi can be reduced to a lower angle

1. Cos (13*pi/12) = cos ( pi + pi/12 ) = - cos ( pi/12)

Find the exact value of cos (pi/12) with the formula :

cos ( 2x ) = 2 * cos² (x) - 1
since you know the exact value of cos (pi/6) ...

2. cos (A+B) = cos(A)*cos(B) - sin(A)*sin(B)
Replace with your x and y.
You already know cos(x), calculate sin(x) with : cos²(x) + sin²(x) = 1.
You could prove that cos(y) = - 3/5 (and sin(y) = -4/5) without noticeable effort (a simple Thales works).

In the end, cos(x+y) = 63 / 65.