Unit Circle Secant

Question

A portion of the unit circle is shown below. Based on this information, determine the value of sec (150) in exact form. Explain how you arrived at your answer.

Answer 1

sec(150) = 1/cos(150)

cos (150) can be read directly from the unit circle.

Your question states only a portion of the unit circle is shown. If only the first quadrant is shown then

cos(150) = -cos(30) and cos(30) is shown on the first quadrant of the unit circle.

cos(30) = sqrt3/2 --> cos(150) = -sqrt3/2 --> sec(150) = -2/sqrt3 or - (2/3)sqrt3

Answer 2

secant of 150 = 1 / cosine(150)

cos(150) = -sqrt(3)/2

The reciprocal is -2/sqrt(3) = -2*sqrt(3)/3 after rationalizing the denominator

(-2/3)*sqrt(3)