The point ( −1/2, −√3/2) lies at the intersection of a terminal arm and the unit circle.
Based on this information, answer the following questions: (6 marks)
a. In which quadrant does the terminal arm lie?
b. What is the measure of the angle? Give the measure in degrees and radians
in terms of 𝜋.
c. Determine exact values for the 6 trig ratios of this angle. Write the ratios in
reduced fractional form with rationalized denominators if necessary.
a. The point (-1/2, -√3/2) lies in the third quadrant.
b. To find the angle, we can use the inverse tangent function.
The angle in radians can be found by:
θ = arctan(-√3/2 / -1/2)
= arctan(√3)
= π/3
The angle in degrees can be found by converting radians to degrees:
θ = π/3 * 180/π
= 60 degrees
c. The trig ratios for the angle θ = π/3 are:
sin(π/3) = √3/2
cos(π/3) = -1/2
tan(π/3) = -√3
csc(π/3) = 2/√3
sec(π/3) = -2
cot(π/3) = -1/√3