Question

Suppose a and b are acute angles with csc(a)=5/3 and cos(b)=8/17. determine the exact values for sin1/2(a) and cos(a+2b)

Answer 1

csc a = 1/sin a = 5/3 -> sin a = 3/5.
To find sin x/2, use the trig identity: cos 2a = 1 - 2si^2 a
cos a = 1 - 2*sin^2 a/2 -> 2sin^2 a/2 = 1 - 8/17 = 9/17
sin^2 a/2 = 9/34 -> sin a/2 = ........
To find cos(a + b) use the trig identity cos (a + b) = cos a*cos b - sin a*sin b
To find sin b and cos a, use the trig identity: cos^2 x + sin^2 x = 1
sin a = 3/5 cos b = 8/17; sin b = .... cos a = .....
Reminder: acute angle means both sin a and cos a are positive.

Answer 2

cos (a + 2b) = cos a*cos 2b - sin a*sin 2b
sin 2b = 2 sin b*cos b =....
cos 2b = 2cos^2 b - 1 = ...

Answer 3

Thank you so much for all this information. What type of answers are you getting? For the second one I got a decimal of .9997890863. I am not quite sure how to write it has a fraction or a fraction of pi. For the first one I got 9/64 or is it 9/17