The trig functions all around the unit circle

In this picture, the angle in the first quadrant closes to the x-axis is labeled a°. It is the upper right hand point of the red rectangle.  (90 - a)° is also in the first quadrant and is the upper right hand corner of the blue rectangle. These two angles are complementary.  The other six angles are some "nice" angle away from a° or (90 - a)°, adding either 90°, 180° or 270°.  All the trig values of sine, cosine and tangent for the eight angles labeled here can be derived from the three values sina, cosa and tana.  We already seen the relationship between the trig values of complementary angles.

sin(90 - a)° = cosa
cos(90 - a)° = sina
tan(90 - a)° = 1/tana

When 90° is added, sine and cosine switch values and the cosine of the new angle is negated as follows.

sin(90 + a)° = cosa
cos(90 + a)° = -sina
tan(90 + a)° = -1/tana

90° more than the complementary angle is the same story with those values.


sin(180 - a)° = sina
cos(180 - a)° = -cosa
tan(180 - a)° = -tana

Adding 180° puts us at the antipode, the polar opposite of where we were.  Sine and cosine will just be negated, while tangent will remain exactly the same.


sin(180 + a)° = -sina
cos(180 + a)° = -cosa
tan(180 + a)° = tana

180° beyond the complement is a similar story.


sin(270 - a)° = -cosa
cos(270 - a)° = -sina
tan(270 - a)° = 1/tana

And then we have adding 270°. This is like adding 180° to the values we got when adding 90°.


sin(270 + a)° = -cosa
cos(270 + a)° = sina
tan(270 + a)° = -1/tana

270° more than the complementary angle is the same story with those values.


sin(360 - a)° = -sina
cos(360 - a)° = cosa
tan(360 - a)° = -tana

Example: 60° is one of our "famous" angles.

sin60° = sqrt(3)/2
cos60° = 1/2
tan60° = sqrt(3)

Find the following values using these three pieces of information.

a) sin150°
b) cos240°
c) tan330°
d) tan 120°
e) sin 210°
f) cos 300°

Answers in the comments.