I have an assignment here on trig equations but I'm not sure how to do them. I have a vague idea but my textbook doesn't offer much help and I won't be able to ask my teacher for assistance until Thursday. Would anybody be willing to explain how they work please?
1) Determine the exact value in simplest form for sin (-135 degrees)/2cos(420 degs) - Sin (240 degs).
I'm just not sure where to begin with this. I thought I'd be able to use the unit circle but it isn't working out.
2) Determine all solutions for each equation:
a) 4cos(3x - 80) + 5.5 = 4.3
b) 8sin^2x+ 10sinx - 3 = 0
What does it mean by "all solutions"?
I thought I'd be able to work it like a normal equation, so I changed A to make 4cos(3x-80) = -1. Then I put my reference angles in quadrants 2 and 3 of the unit circle, got ref angle = cos^-1 (1) and couldn't do anything else because my calculator can't solve it. What'd I do wrong? It's the same story with B; I work it as far as the ref angle and my calculator tells me I'm doing it wrong.
3) Determine the x intercepts of the function f(x) = 6sin [3/4 (x-120)] + 5 on the interval xE[-360, 360].
That one completely goes over my head. I'm pretty sure I'm supposed to create a graph for it, but I dont' even know where to begin. What does it want? And what does "on the interval xE[-360, 360]" mean?