Question

If f(x)=sigma (sin^2 (x))^k from k=1 to infinity, then f(1) is?

Answer 1

@Hero @zepdrix @abb0t @Compassionate

Answer 2

@tkhunny @beccaboo333 @Destinymasha

Answer 3

I am not good with this kind of math. I'm sorry :/

Answer 4

It's alright.

Answer 5

The ONLY x appearing in the definition is int he sine function. Substitute in there and see what you get.

\(\sin(1) = 0.84147\)

\(\sin^{2}(1) = 0.70807\)

That's it. Now, use all you know about Geometric Series and add it up!

Answer 6

\[
\sum _{k=1}^{\infty } \sin ^{2
k}(x)=\tan ^2(x)
\]
Do you know how to do it?

Answer 7

Your answer is
\[
\tan^2(1)=2.42552
\]

Answer 8

But the answer should be 2.400.

Answer 9

Yes to the nearest 10th

Answer 10

This is a multiple choice problem with the answer choices a) 0.369, b) 0.585, c) 2.400, d) 2.426, and e) 3.426 and the answer is D.

Answer 11

select 2.400

Answer 12

But how to get there?

Answer 13

\[
\sin^2(x) + \sin^4(x) +\sin^6(x) + \cdots=\\
\sin^2(x)(1 + \sin^2(x) +\sin^2(x) + \cdots=\\
\sin^2(x)\frac 1{1- \sin^2(x)}=\frac {\sin^2(x)}{\cos^2(x)}=\tan^2(x)

\]
It is a geometric series. We need to assume \[\Large
\left|\sin^2(x) \right|<1

\]

Answer 14

Do you understand now?

Answer 15

I understand now. Thanks for helping me in this late night. I appreciated it.