## anonymous one year ago How would you simplify tan(sin^-1 (x/2)) to find its exact value? Is sin^2 theta+cos theta=2 true or false?

1. anonymous

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2. anonymous

there is a picture of an angle whose sine is $$\frac{x}{2}$$ find the third side via pythagoras then you can find any trig ratio you want

3. anonymous

Does it matter that it's sin^-1?

4. anonymous

not sure what you are asking but i guess the answer is "of course it matters" if it was cosine it would be different

5. anonymous

did you find the third side?

6. anonymous

i think maybe i lost you there ?

7. anonymous

Sorry, I spent some time doing the calculation with identities instead of a triangle and ended up with $\tan(\sin^-1 x/2)= (x/2)/(√1-(x^2/4))=x/(2√(1-(x^2/4)))$ Would this result in the same answer as using the triangle?

8. amilapsn

yep