Question

1) Find the values (if possible) of the six trigonometric functions of o if the terminal side of o lies on the given line in the specified quadrant.

y=1/3x

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

(a) 10pie/3
(b) 17pie/3

Answer 1

1) A y = x/3 line makes an angle of arctan 1/3 with the x axis. That line is in the first quadrant (and also the third quadrant).

You have not specified the quadrant.

tan theta = 1/3, by definition
sin theta = 1/sqrt10 (in the 1st quadrant)
cos theta = 3/sqrt10
etc.

2) (a) Subtract 2 pi from 10 pi/3 you will see that it has the same trig functions as 4 pi/3. The reference angle is pi/3 and it is in the third quadrant. The cosine is -1/2 etc. You should be able to figure out the others.

(b) Subtract 4 pi = 12 pi/3 and you get
5 pi/3 . The reference angle is pi/3 and it is in the fourth quadrant. The cosine is 1/2, etc