Posted by **Hannah** on Wednesday, February 10, 2010 at 4:40pm.

1) Evaluate (if possible) the sine, cosine, and tangent of the angles without a calculator.

a) 10pi/3

Sin = -sqrt 3/2

Cos = -1/2

Tan = sqrt 3

Are these correct ? I do not understand when to make them negative.

b) 17pi/3

Sin = -sqrt 3/2

Cos = 1/2

Tan = - sqrt 3

Are these correct?

- Pre-cal (Please Check) -
**Reiny**, Wednesday, February 10, 2010 at 5:16pm
your answers are correct, (but I have a feeling you used your calculator and then decided what radical your answer was)

Some students find it easier to "think" in degrees than radians

10pi/3 radians = 600

you have to change that to a co-terminal angle, that is, an angle in the first rotation landing in the same position.

To do that subtract multiples of 360 until you have an answer less than 360

600-360 = 240

Now ask yourself, "Where is 240 ?"

- in the third quadrant.

In III, the sine is -, the cosine is +, and the tangent is +

Now ask yourself, "What is the angle in standard position equal to 240 ?"

- that is, how far to the x-axis ? -- 60

You should know the sine, cosine and tangents of 60

Using the proper sines for III

sin 10pi/3 = sin 600 = sin 240 = -sin 60 = -√3/2

etc.

Practice with a few, after a while this is very quick and easy.

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