Can someone please help me with trig formulas? I have a big test tomorrow. I will FAN and MEDAL

Question

freckles · Answer

Do you know what you need help on exactly?

anonymous · Answer

$$\cos (\sin^{-1} \frac{ 2 }{ 3 } + \tan^{-1}  \frac{ 3 }{ 2 })$$
I need to find the exact value

freckles · Answer

let a=arcsin(2/3) and let b=arctan(3/2)
so sin(a)=2/3    and tan(b)=3/2
build two right triangles using that info


now to expand cos(a+b) and use those triangles to evaluate cos(a+b)
we will need the identity:
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

anonymous · Answer

I dont understand the first part you wrote but I get the formula

freckles · Answer

hmmm... do you mean you don't know what the arc part is ?

basically I said let $$a=\sin^{-1}(\frac{2}{3}) \text{ and } b=\tan^{-1} (\frac{3}{2})$$

anonymous · Answer

Oh okay I see it now

anonymous · Answer

would I leave the cos from the formula in when I input the alpha

freckles · Answer

what?
not sure what you are saying 
have you found cos(a) given sin(a)
and have you found cos(b) and sin(b) given tan(b)?

freckles · Answer

en example:
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