`sec(theta) = 2` Find two solutions of each equation. Give your answers in degrees (0 <= theta <= 360) and radians (0 <= theta <= 2pi)

shmindle | Student

Since sec is just 1/cos, sec(θ)=2 can also be written as 1/cos(θ)=2.

By multiplying and dividing, you'll get to cos(θ)=1/2.  

On the unit circle, always think of the x axis when referring to cosine.  At the 1/2 mark on the x axis, draw a vertical line that is parallel to the y axis.  Where this vertical line and the circle meet are your 2 answers between 0 and 360 degrees and 0 and 2pi.

In the first quadrant, there is your first solution— 60°, or pi/3 radians.

Your second solution is in the fourth quadrant— 300°, or 5pi/3 radians.

The attached unit circle chart may be of use.

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