Question

1) Find two values of Q that satisfy the equation. Give your answer is degrees and radians. Do not use a calculator.

a) sec Q = 2

-pi/3 and 60 degrees

Is this correct?

b) sec Q = -2

This one I do not know how to find.

Answer 1

I will do the second one.

The first thing I do is to change the expression into one of the 3 basic trig ratios.
sec Q = -2 -----> cos Q = -1/2

I then find the "angle in standard position", which is the angle it the first quadrant.
You have to know your 30-60-90 and your 45-45-90 ratio of sides.
we know cos 60º = 1/2

From the CAST rule, I know that the cosine is negative in quadrants II and III
so Q = 180 - 60 = 120º (quadrant II)
or
Q = 180 + 60 = 240º (qudrant III)

of course in radians that would be 2pi/3 and 4pi/3

Now redo the first one, you are missing an angle. (where else is the cosine positive ?)