Question 172288: Would someone please show me how to do these two problems. I have no textbook.
1. P(-15/17,-8/17) is found on the unit circle. Find sin O (theta) and cos O(theta).
2. Solve: x=Arctan(-sq. root 3).
I have to show all my work
Thanks
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! P(-15/17,-8/17) is found on the unit circle. Find sin O (theta) and cos O(theta).
On a unit circle, the hypotenuse is always 1.
The sine is the y, and the cos is the x.
sin = -8/17
cos = -15/17
The angle wasn't asked for, but it's ~208º or -152º
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2. Solve: x=Arctan(-sqrt(3))
tan = sin/cos = sqrt(3) --> sin = sqrt(3)*cos
sin^2 + cos^2 = 1 (1 is the hyp of the unit circle)
(sqrt(3)*cos)^2 + cos^2 = 1
3cos^2 + cos^2 = 1
4cos^2 = 1
cos^2 = 1/4
cos = 1/2
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The arccos(1/2) is 60 degs, so the angle is 60 degs.
tan(60) = sqrt(3)
Since it's negative, it's in quadrant 2 or 4
tan(120) = -sqrt(3)
tan(300) = -sqrt(3)
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Is that sufficient?
I have to show all my work
Thanks
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