## anonymous one year ago How can I simplify.... tan(arcsin x) ??

1. anonymous

tan= sin/cos

2. anonymous

Yep, so does it become... $\frac{ \sin(\sin^{-1} x) }{ \cos(\sin^{-1} x) }$ ??

3. anonymous

and then $\frac{ x }{ \cos (\sin^{-1}x) }$

4. anonymous

yes

5. anonymous

Is that the furthest I can simplify?

6. anonymous

i think no

7. anonymous

Do have any hints on what I can do?

8. geerky42

9. geerky42

Let there be a triangle with opposite side of $$x$$, and hypotenuse of $$1$$. By Pythagorean Theorem, adjacent side would be $$\sqrt{1-x^2}$$. |dw:1433108189889:dw| From here, we can see that $$\sin\theta = \dfrac{x}{1} = x$$, hence $$\theta = \arcsin(x)$$ Now, what is $$\tan\theta = \tan(\arcsin(x))$$?

10. geerky42

Remember SOH CAH TOA?

11. anonymous

Ohh so tan is opposite/adjacent .... so $\frac{ x }{ \sqrt{1-x^2} }$

12. geerky42

Gotcha

13. anonymous

Awesomeness!! XD

14. anonymous

Thanks so much @geerky42

15. geerky42

Welcome!