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Learning trigonometry right now.

I have a question that asks:

Write the trigonometric expression in terms of sine and cosine, and then simplify:

$$(\cot^2\theta + 1) \sin^2\theta$$

I know the answer is $1$. I'm confused on how to get there. I have:

$$(\cot^2\theta+1)\sin^2\theta = \csc^2\theta\sin^2\theta$$

Nathaniel Bubis
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munchschair
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    Could you let us know how far you have got, and where you are getting stuck? – Old John Dec 01 '13 at 21:33
  • OK - do you know the definition of $\csc$? – Old John Dec 01 '13 at 21:39
  • Because I have a sheet of identities. cot^2θ+1 = csc^2x – munchschair Dec 01 '13 at 21:41
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    That is not the definition of $\csc$ that I use! Do you know a definition of $\csc$ in terms of $\sin$? – Old John Dec 01 '13 at 21:42
  • cscx = 1/sinx ? – munchschair Dec 01 '13 at 21:43
  • Yes - can you finish the problem using that? – Old John Dec 01 '13 at 21:44
  • WOAH, thank you very much. Is there a way to give you points? I use stackoverflow to help me in programming and trig is the first wall I've hit learning math. I know if you give an answer, I can confirm it. – munchschair Dec 01 '13 at 21:47
  • No worries - I don't need points. Glad to help. – Old John Dec 01 '13 at 21:51
  • One other question:

    I have to simplify: sinx cos^2 x + sin^3 x

    My guess is that it becomes sin^2 x. But it's marked wrong. I used the pyhtagorean identity of sin^2 x + cos^2 x = 1 to get there.

     – munchschair Dec 01 '13 at 22:06
  • Take out a factor of $\sin x$: to get $\sin x \cos^2 x + \sin^3 x = \sin x (\sin^2 x + \cos^2 x) = \sin x (1) = \sin x$. If you get any more, maybe drop into the chatroom? – Old John Dec 01 '13 at 22:08
  • Lol that seemed so obvious looking at it now. I'll see how far I get. – munchschair Dec 01 '13 at 22:16
  • @OldJohn While you may not want reputation points for helping munchschair, it would still be good to get this out of the unanswered queue. I recommend either munchschair answers it themself or you answer community-wiki, and either way munchschair accepts it. – Mark S. Dec 01 '13 at 22:48
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    Gotta say math.stackexchange is a lot friendlier then stackoverflow. People aren't very big on letting things like formatting slide on nubes. Thanks ya'll. – munchschair Dec 02 '13 at 00:41

1 Answers1

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For the question in your main post, you are nearly there:

$$(\cot^2\theta+1)\sin^2\theta = \csc^2\theta\sin^2\theta$$

and now just use the definition that $\csc\theta = 1/\sin\theta$ to get:

$$\csc^2\theta\sin^2\theta = \frac{1}{\sin^2\theta}.\sin^2\theta = 1$$

For the question in the comments:

$$\sin x \cos^2 x + \sin^3 x = \sin x (\sin^2 x + \cos^2 x) = \sin x . (1) = \sin x$$

Old John
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