Quick question on Trigonometry.

Parasite1230

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The last part of this question I cannot figure out how to solve. I have the answer available to me but I don't know how it was achieved.
 

mmm4444bot

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Your image is unreadable. The resolution is too low or the dimensions are too big.

Please try hosting your image at imgbb.com

Alternatively, you can type the exercise into your post.

Please also show any work that you already tried or explain why you're stuck.

Thank you. :cool:
 

Dr.Peterson

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The last part of this question I cannot figure out how to solve. I have the answer available to me but I don't know how it was achieved.
Straining my eyes, it looks like the last question is equivalent to:

For what numbers \(\displaystyle x\), \(\displaystyle -2\pi\lt x\le2\pi\) does \(\displaystyle 5\sin x = -\frac{5}{2}\)?​

This is a reasonably simple equation to solve. Please show whatever you are able to do (for example, find one solution), and tell us why you are stuck there. We need to know what you are able to do, in order to guide you into what you can't yet do.
 

Parasite1230

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Update

Assignment with proper questions: https://ibb.co/nBwmcRf
My work on grid paper: https://ibb.co/2nc20Tp
I graphed the sin function with the proper transformation and know how to get everything except for f) where it says f(x)=-5/2. Am I supposed to find it out purely from the graph or did I plug it in wrong to the original function?
 

Dr.Peterson

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Assignment with proper questions: https://ibb.co/nBwmcRf
My work on grid paper: https://ibb.co/2nc20Tp
I graphed the sin function with the proper transformation and know how to get everything except for f) where it says f(x)=-5/2. Am I supposed to find it out purely from the graph or did I plug it in wrong to the original function?
Thanks for the update. The image of your worked is washed out, but you seem not to have followed my hint.

It is not asking you to find f(-5/2), which you wrote near the bottom, but to solve f(x) = -5/2. That is, -5/2 is a value of y, not of x.

So you have to solve 5 sin(x) = -5/2, which simplifies to sin(x) = -1/2. The answer (principal solution) is one of the "special angles" you should recognize. Then you can use ideas from the graph, or other means, to see the other solution(s).
 

mmm4444bot

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Parasite1230

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Final Update

Thank you for the help! I guess it was just a concept problem. I now understand. Just need to use the information given to find out the critical points of sinx = -1/2 on the unit circle. Since Sin = y/r, i know to associate it with the y coordinate points that are -1/2 on the bottom half of the unit circle and the points in the other half but flipped with a (-).
 
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