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Question
Find the exact value of the sine, cosine, and tangent of 210.

and

Find cot (290).

Point P is located at the intersection of a circle with a radius of r and the terminal side of an angle θ. Find the coordinates of P to the nearest hundredth. θ = 120 , r = 13

Answer
Questioner:adelefair
Country:New Jersey, United States
Category:Advanced Math
Private:No
Subject: algebra II

Question:
Find the exact value of the sine, cosine, and tangent of 210.


For this, you will make a (very accurate) diagram, with the terminal side winding up in quadrant II. (-90 gets you to 'down', -180 gets you to 'left' and another 30 degrees (the key number) gets you to quadrant II.

Then you use your knowledge of the 30-60-90 triangle and put  x = -sqrt(3)/2,  y = + 1/2, and r = 1.  Now you can use the basic definitions.

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Find cot (290).

This will wind up in quadrant I (isn't -290 coterminal with -290 + 360 = +70?)

So this is cos 70/sin 70  [remember those quotient identities?]

OR: this is 1/tan 70. [remember those reciprocal identities?]

and you will need your calculator.
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Point P is located at the intersection of a circle with a radius of r and the terminal side of an angle θ. Find the coordinates of P to the nearest hundredth. θ = 120 , r = 13

Use the definitions:

sin θ = y/r,  so  y = r sin θ
cos θ = x/r,  so  x = r cos θ

You can handle the rest. Either:

120 is in Quadrant II, and the 'reference angle' is 60, and you will do the same stuff as in the first problem.  THAT had r = 1, so you will just multiply all by 13.  You'll need the calculator for sqrt(3), of course.

or:

use your calculator for sin 120  and  for cos 120

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