(Solved) For each of the following values of cos θ, determine the radian value of θ if pi ≤ θ ≤ 2pi

marinejas

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3 years ago Edited: 3 years ago, marinejas

For each of the following values of cos θ, determine the radian value of θ if pi ≤ θ ≤ 2pi

Hi! sorry for coming back to this section again, but I have another question similar to this, so the question is "For each of the following values of cos θ, determine the radian value of θ if pi ≤ θ ≤ 2pi". I got a) right, but not b) for b) the question is -√2/2 and this is what I did.
cos = -√2/2
cosine is negative in quads 2 and 3, angle used 3pi/4
2nd quad
pi - 3pi/4 = 1/4pi
3rd quad 3pi/4 - pi = -1/4pi
But the answer was 5pi/4.
I even tried doing it in a diff way I did angle pi/4
2nd quad
pi - pi/4
= 3/4pi
3rd quad
pi/4 - pi
= -3/4 pi

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bio_man

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3 years ago

Hi marinejas, make sure you start a new topic every time a new question arises. Let me separate this one for you

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bio_man

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Educator

3 years ago

OK, so look at the range. They want answers between PI and 2PI, suggesting quadrants 3 and 4. They're not interested in quadrant 2.

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marinejas Author

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3 years ago

but cosine is negative in quads 2 and 3? I'm using the unit circle as a reference and the x is cosine and y is sin so wouldn't that mean the overall angle that gives the ratio... of √2/2 is 3pi/4?

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bio_man

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Educator

3 years ago

Look at the restriction: pi ≤ θ ≤ 2pi, what does this tell you? They're ONLY interested in stuff that happens in quadrants 3 and 4. As you mentioned, cosine is negative in quadrant 3. So ONLY report the answer that is found in quadrant 3.

Let me know if you want me to show you

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marinejas Author

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3 years ago

including the 1st quad? bc I used the 1st and 4th quad for a) and I got the answer.

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bio_man

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marinejas Author

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3 years ago

don't you mean ignore 3rd quad? and also is it possible for you to bring back the other questions/stuff from this same question, just want to look back at it, thanks.

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bio_man

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Educator

3 years ago

If the question is "For each of the following values of cos θ, determine the radian value of θ if pi ≤ θ ≤ 2pi"

Then definitely you focus on the lower half the x-y plane -- there's no question about it.

Was my answer right based on the books expected answer? The other topic is still available, just look at the index of this board > https://biology-forums.com/index.php?board=33.0

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marinejas Author

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3 years ago Edited: 3 years ago, marinejas

oh okay sorry, and yes the answer was right.

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bio_man

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#10

Educator

3 years ago

Sounds to me like you're still struggling with this stuff Frowning Face

I'll be around if you have more questions

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marinejas Author

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#11

3 years ago

oh no I got it now, I redid both questions

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bio_man

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