The other tutor just blurted out the answers.
Here is how we learn to come up with them:

Change  to degrees:



Add 360°: -150°+360° = 210°

That's in QIII, so we draw the angle:



The reference angle is the acute angle between the 
radius vector and the x-axis.  So for 210°, the
reference angle is gotten by subtracting 180°
from it, getting 210°-180° = 30°

Then we learn the 5 special angles, by memorizing this chart:

  

If we want sine we read from the left across with the angles
at the top, and if we want cosine we read from the right across
using the angles at the bottom:

Then we memorize:

"All Students Take Calculus", which is a mnemonic device 
that is used to help students memorize the sign values 
of all the trigonometric functions in the 2-dimensional 
Cartesian coordinate system. The letters ASTC signify 
which of the trigonometric functions are positive, 

in the order of the quadrants - starting in the top 
right quadrant, and moving counterclockwise.

In Quadrant I: A for All - all trigonometric functions 
are positive in this quadrant.

In Quadrant II: S for Sine - sine and cosecant functions 
are positive in this quadrant.

In Quadrant III: T for Tangent - tangent and cotangent 
functions are positive in this quadrant.

In Quadrant IV: C for Cosine - cosine and secant functions 
are positive in this quadrant. 

So therefore both the cosine and sine are negative in 
quadrant QIII.



and



Edwin