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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

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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