Question

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 15 years ago

Answer 1

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

Answer 2

or maybe It is 9√(1-sinθ^2)...

Answer 3

yes

Answer 4

your second post was right

Answer 5

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

Answer 6

next you need to figure out which trig substitution to use

Answer 7

Thank you! would the answer be 9cscθ then?

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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
?

Answer 12

ok so 9cosθ?

Answer 13

yes :)

Answer 14

Sweet! thanks a bunch!