Question

1) Find the exact value of cos 105 degrees by using a half-angle formula.

2)Find the solution of sin 2theta = cos theta if 0 degrees</= theta < 180 degrees.

I have read the book and looked at the examples, but cannot figure out how to work these. Any help would be great!!

Thanks

Answer 1

1)
105 * 2 = 210 is a nice angle, 180 + 30

2)
2 sin t cos t = cos t
2 sin t = 1
sin t = 1/2
t = 30 degrees or pi/6 radians

the other solution t = 150 degrees is no good because the cos t would be negative