How Do You Solve Complex Trigonometric Problems?

[esploded]

1. Hi, I have a pre-calculus final tomorrow, and there are a few questions I don't understand.
I'd truly appreciate it if you could help :)

1. If sin(theta)=1/4, theta in quadrant II, find the exact value of cos(theta+pi/6)

2. sin(sin^-1(2/3) + cos^-1(1/3)) -- simplify

3. cos(5pi/18)sin(pi/9) - cos(pi/9)sin(5pi/18) -- simplify


2. n/a



3.

1. if sin theta = 1/4, that would mean the sides are 1, 4, root15. Use coscos-sinsin (composite argument) and plug into make [(root 15)/4 * root3/2 ] - [1/4 * 1/2] then...?

2. I'm truly confused about this one... do you use the calculator to find the individual inverse sine/cosine functions? then add the two, and use the sin function on them? If so, do you use the graphing calculator?

3. this is the sine composite function (subtracting), I know that, but I do not know how to continue on...




I am so bad at these, and I'm freaking out for my final... :(

Thank you!

 

[SammyS]

θ is in Quadrant II, so cos(θ) is negative.

 

[QuarkCharmer]

For #3, just take a look at the sum/difference identities:

Once you have it in the form sin(x-y), it should be easy to simplify..