Can you help me with these? (Advanced Math)?

Question

1) tan(345°)= -2 -(square root of 3)
2) csc(915°)
3)tan((-7pi)/(12))
4)sec(pi/12)
5)sin(x-y) if cos x=(8/17) and cos y = (3/5)
6) tan (x-y) if csc x = (13/5) and cot y= (4/3)


We had those for a test a few weeks ago, but i still don't quite understand them. I know how to work them, but i am doing something wrong along the way. If you could please work these out and show your work, i would greatly appreciate that. Thanks!!

Answer 1

You say you know how to work them but are doing something wrong along the way.

why don't you show us what you did so we can give you specific feedback?

Answer 2

5 sin (x-y) = sinx cosy - cosx siny

and if cosx = 8/17 (assuming x and y are in quadrant I), sinx = 15/17 (from Pythagorean theorem; 17^2 - 8^2 = 225 = 15^2. Likewise, sin y = 4/5. So plug those in. But be sure it didn't say what quadrant x and y are in because the signs would change.

Answer 3

1)
tan(345)
= tan(345-360)
= tan(-15)
= tan(30-45)
= [tan30 - tan45]/[1 + tan30 tan45]
= [1/sqrt(3) - 1]/[1 + 1/sqrt(3)]
= [1 - sqrt(3)]/[sqrt(3) + 1]
= [1 - sqrt(3)]^2/(-2)
= [4 - 2sqrt(3)]/(-2)
= -2 + sqrt(3)

2)
csc(915)
= csc(195+720)
= csc(150+45)
= 1/[cos150 cos45 - sin150 sin45]
= 4/[-sqrt(6) - sqrt(2)]
= -sqrt(6) + sqrt(2)