Our teacher says that this unit (identities and formulas) is the hardest, and I'm starting to believe him haha. Anyways, I need some assistance on a few problems (please excuse my poor English):
1. solve 2sinē(y)-5sin(y)=-3
I factored and found that sin(y)=1 and sin(y)=3/2. Because sin(y)=1, I concluded that one of the solutions must be pi/2. However, with the sin(y)=3/2, that is not a special triangle, so how do I find the solutions?
2. Verify: cos(y+pi)=-cos(y)
I'm completely stumped. I know that there is an identity cos((pi/2)-x)=sinx, but that's the closest I could find...
3. solve 2cotē(y)+3csc(y)=0
I factored and found csc(y)=-2 and csc(y)=-1. Therefore, I found the solution set to be (3pi)/2, (7pi)/6, and (11pi)/6. I plugged in the answers in the original problem to check, and while (7pi)/6 and (11pi)/6 work, (3pi)/2 doesn't. I derived the answer choice (3pi)/2 from the csc(y)=-1; if csc(y)=-1, then shouldn't sin(y) also equal -1, therefore making (3pi)/2 a valid answer?
4. tan(y)=3/4 and sin(y)<0, what is sin(2x)?
I know that this must be located in the quadrant III but that's as far as I've got. It's a 3,4,5 triangle, but I don't know the angle.
5. find the solutions in [0,2pi) for sin(2y)+sin(y)=0.
I was thinking that you might factor this to be sin(2y+1), but I'm not completely sure. I know that sin(2y) includes multiple angles but I can't seem to find the solution.
Thanks in advance guys