cos(1950°)

We use the fact that we can add or subtract any integer times 360°
to an angle and get a coterminal angle that has the same trig
ratios. 

So we divide 1950° by 360°


       5
360)1950
    1800
     150

So we can subtract 5×360° or 1800° from the angle and still have an
angle with the same cosine:

So cos(1950°) = cos(1950°-1800°) = cos(150°) = 

----------------



We use the fact that we can add or subtract any integer times 
to an angle in radians and get a coterminal angle that has the same trig
ratios:

So we divide  by 

.

If we added only 5 times  to the angle, we would get a negative angle,
so we must add 1 more than 5 or 6 times  to get a positive angle.

So we add  or  to the angle and get a positive angle
with the same cosecant:



Edwin