The first one isn't so much a trig identity as it is a definition:Originally Posted by Liyo
For the second one, we use probably the most standard trig identity:
So if we have the cosine...
Now, we are looking for an angle between 90 and 180 degrees. The sine function is positive in this interval. So . Specifically, we will be finding a value for theta between 0 and 90 degrees, so we are considering the angle we will find to be a reference angle.
I don't know of any "nice" angle such that the sine of theta will be this value. So find theta using a calculator. Now, this is the reference angle measured from 180 degrees, so we subtract this angle from 180. I get about 131.8 degrees.