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May 9th, 2013, 05:01 PM   #1
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Find sine and cosine of given value

Hi,

If and , find the sine and cosine of the given value.

OK, the point lies in quadrant IV. I know this because sine is negative and cosine is positive.





Moved ? units anticlockwise from quadrant IV.





The x-coordinate stays the same, but the sign of the y-coordinate changes.





Moved 90 degrees from quadrant IV anticlockwise.





Moved 90 degrees anticlockwise from quadrant I.
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May 9th, 2013, 05:43 PM   #2
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Have you checked your answers by using a calculator?
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May 9th, 2013, 06:44 PM   #3
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Quote:
Originally Posted by skipjack
Have you checked your answers by using a calculator?
I am not sure how to.
For d. the calculator gave two positive answers. Is that correct?

The concepts aren't really firm in my mind. If I sort that out, the calculator steps should follow.
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May 10th, 2013, 01:27 AM   #4
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Are you saying you don't know how to use your calculator to find a value for t in the fourth quadrant that satisfies the equation ? It would suffice to evaluate If you get that right, you should find that cos(t) = 1/3.

In your answers, are you listing the sine first or the cosine first?
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May 10th, 2013, 02:05 AM   #5
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Quote:
Originally Posted by skipjack
Are you saying you don't know how to use your calculator to find a value for t in the fourth quadrant that satisfies the equation ? It would suffice to evaluate If you get that right, you should find that cos(t) = 1/3.

In your answers, are you listing the sine first or the cosine first?
Thank you.

Isn't there a particular concept behind this sort of problem?

I was focused on solving it another way. Can't it be done without a calculator?
That would be ideal for my learning.

Cosine first.
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May 10th, 2013, 02:13 AM   #6
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I assumed that you had already obtained your answers without use of a calculator (probably by using standard trigonometric identities). That's why I suggested using a calculator to check your answers. If you post all your reasoning (for example, explaining how you used "moved 90anticlockwise"), the specific errors you have made can be identified. Note that it doesn't suffice to establish the quadrant in which the angle lies, although you could use that to check that your answers have the correct sign.
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May 10th, 2013, 02:35 AM   #7
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Quote:
Originally Posted by skipjack
I assumed that you had already obtained your answers without use of a calculator (probably by using standard trigonometric identities). That's why I suggested using a calculator to check your answers. If you post all your reasoning (for example, explaining how you used "move 90 anticlockwise), the specific errors you have made can be identified.




I think of the point t as being somewhere in quadrant 4 because of the signs of the coordinates.
Starting at initial angle of 2?, then moving in an anticlockwise direction because ? is positive.
This leads me to quadrant II where cosine is negative and sine positive.



For this I used the cosine and sine function only because it's the only way I know to solve this type of problem.



Move a quarter of the way around the circle from (1,0) in an anticlockwise direction because ?/2 is positive.



This is point is in quadrant II, so moving from there to in an anticlockwise direction by ?/2 units leaves in quadrant III.
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May 10th, 2013, 02:59 AM   #8
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For (a), adding ? takes you from the fourth quadrant to the second quadrant.

For (b), you don't specify the quadrant. Your explanation isn't detailed enough to explain your answers.

For (c), adding ?/2 takes you from the fourth quadrant to which quadrant?

For (d), your explanation mentions two quadrants. The wording doesn't make sense and leaves it unclear which quadrant is determining your answers.
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May 10th, 2013, 04:03 AM   #9
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Quote:
Originally Posted by skipjack
For (a), adding ? takes you from the fourth quadrant to the second quadrant.

For (b), you don't specify the quadrant. Your explanation isn't detailed enough to explain your answers.

For (c), adding ?/2 takes you from the fourth quadrant to which quadrant?

For (d), your explanation mentions two quadrants. The wording doesn't make sense and leaves it unclear which quadrant is determining your answers.
b. cos (-t) = cos t; sin(-t) = -sin t.


c. ?/2 lands in the first quadrant.



d. Adding ?/2 to -t in the first quadrant brings me to quadrant II.

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May 10th, 2013, 04:52 AM   #10
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Re: Find sine and cosine of given value

For c, see here. See if you can figure out why these identities are true.
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