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anonymous

  • one year ago

I'm really struggling with establishing identities and I would seriously love some help. Here are two questions I need answered: https://i.imgur.com/BnFBQ33.png and https://i.imgur.com/nK2VeCH.png I'm not sure where to start with either of these, and I really would like to know how to solve them and what the answers are. Any advice would be helpful! Thanks in advance!! :)

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  1. anonymous
    • one year ago
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    does it help to know that \[\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}\]?

  2. anonymous
    • one year ago
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    Yes! I found a sheet of a few things like that but I'm not exactly sure how they work. http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

  3. anonymous
    • one year ago
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    so for the first one \[\cos(\theta)\tan(\theta)=\cos(\theta)\frac{\sin(\theta)}{\cos(\theta)}=\sin(\theta)\]

  4. anonymous
    • one year ago
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    it is mostly algebra the cosines cancel

  5. jim_thompson5910
    • one year ago
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    They have the answer choices written out in one long line, which makes it a bit tricky to sort things out. I find it better to have it written out like this \[\Large \cos(\theta)\tan(\theta) = \sin(\theta)\] \[\Large \cos(\theta){\color{red}{\tan(\theta)}} = \sin(\theta)\] \[\Large \cos(\theta){\color{red}{\frac{\sin(\theta)}{\cos(\theta)}}} = \sin(\theta)\] At this point, I'm sure you see what cancels. Throughout the whole process, the right side stays the same.

  6. anonymous
    • one year ago
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    the second one is completely different it is derived from the "subtraction angle" formula \[\sin(\alpha-\beta)=\sin(\alpha)\cos(\beta)-\cos(\alpha)\sin(\beta)\]

  7. anonymous
    • one year ago
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    put \(\alpha=\frac{\pi}{2}\) and \(\beta=\theta\) and you get it

  8. anonymous
    • one year ago
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    Okay, I think I get the canceling thing. One the first one at least. for the first question would the answer would be B since the \[\cos()\] cancel out and \[\tan( \theta)\] equals sin over cos, which equals the others. Is this correct?

  9. anonymous
    • one year ago
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    Sorry for the weirdness, I'm not super sure how to use the equation button. I meant: \[\cos (\theta)\]

  10. jim_thompson5910
    • one year ago
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    yes the first one is B

  11. anonymous
    • one year ago
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    I'm still a little stuck with the second question. Would it be C since the subtraction angle formula comes out to be sin(π/2−θ)=sin(π2)cos(θ)−cos(π/2)sin(θ) which matches the first part of the equation? Some of this stuff is going over my head.

  12. jim_thompson5910
    • one year ago
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    You have it correct.

  13. anonymous
    • one year ago
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    Thanks both of you! :3

  14. jim_thompson5910
    • one year ago
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    you're welcome

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