## anonymous 5 years ago Can someone help me finish this problem I took it as far as I could... If x=9sinθ, use trigonometric substitution to write √(81-x^2) as a trigonometric function of θ, where -pi/2<θ<pi/2.

1. anonymous

So far I have √(81-9sinθ^2) 81√(1-sinθ^2) 1-sin^2θ=1/cscθ ?

2. anonymous

or maybe It is 9√(1-sinθ^2)...

3. anonymous

yes

4. anonymous

5. anonymous

√(81-81sinθ^2) <--- (9sinθ)^2 = 81sinθ^2 = 9√(1-sinθ^2)

6. anonymous

next you need to figure out which trig substitution to use

7. anonymous

Thank you! would the answer be 9cscθ then?

8. anonymous

$\sin ^{2}\theta+\cos ^{2}\theta = 1$ is a where you want to start thinking about your substitution

9. anonymous

the answer isn't 9cscθ, but you are almost there

10. anonymous

use $1-\sin ^{2}\theta = \cos ^{2}\theta$

11. anonymous

oh ok...where did the cos come from? I thought sinθ=1/cscθ so in this case it would be 1-sin^2θ=1/cscθ ?

12. anonymous

ok so 9cosθ?

13. anonymous

yes :)

14. anonymous

Sweet! thanks a bunch!