Precalculus/Trigonometric Functions of Sine, Cosine, and Tangent with given parameters? for my precalculus class I was given an assignment for extra credit however it is some material that I have yet to cover or learn as far as sine, cosine, and tangent go. Below is the prompt that I was given:

If sin α = 3/13 where 0 &lt; α &lt; π/2 and cos β = -2/9 where π &lt; β &lt; 3π/2, determine the following:


sin(α - β)
cos(β - α)
tan(2β)
cos(4β)
cot(α + β)


I am not quite sure of the first step to take on these. I wasn't able to find much online either due to my search terms or what not. I hate to upload such a blank question however I am at a loss for how to approach these questions...
They require you to use the identities: $$\sin(\alpha\pm \beta)=\sin \alpha \cos \beta \pm \cos \alpha \sin \beta$$ $$\cos (\alpha\pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta$$
From these one can infer the double-angle formulae:
$$\sin 2\alpha = 2\sin \alpha\cos \alpha$$ $$\cos 2\alpha = \cos^2 \alpha -\sin^2 \alpha = 2\cos^2 \alpha -1 =1-2\sin^2 \alpha$$ $$\tan 2\alpha = \frac {2\tan \alpha}{1-\tan^2\alpha}$$
To find the value of $\sin\beta$ or $\cos\alpha$, draw a triangle with the lengths of two sides given by the fractions $\frac 3 {13}$ or $\frac {-2} 9$. Use Pythagoras' Theorem to find the length of the third side, and infer the value of $\sin\beta$ or $\cos\alpha$. 



You could use the CAST diagram to work out whether $\sin\beta$ and $\cos\alpha$ are positive or negative, by looking at where the angles $\alpha$ and $\beta$ lie in a circle.
If you want calculate this, you can use this site: http://www.milefoot.com/math/trig/22anglesumidentities.htm.

With those formulas your work is just analyze the signals of the functions in these intervals, can you do it or you don't know how analyze the signals ?