Question

Find the angle in standard position whose cosine is 1/2

A 5π/3
B π/3
C π/3 and 5π/3
D 4π/3 and 2π/3

Answer 1

C is the correct answer

Explanation:

In this question, we are tasked with calculating the angle at standard position which has a cosine value of 1/2

With reference to the cartesian coordinates, there are only two quadrants which has positive valued for Cosine. These are the first quadrant and the last or 4th quadrant. While the first quadrant has angles in the range of 0-90 the fourth quadrant has an angle range from 270-360

Now back to the angle. In the first quadrant, the angle that has cosine value equal to 30 is cos 60. This is same as pi/3 radians

Now the general form of the angle on the fourth quadrant is 360-theta

Thus, since our theta is pi/3, which is 60, that angle on the fourth quadrant having same value as 1/2 is 360-60 = 300

This is same as 5pi/3 radians

So our answers are pi/3 radians and 5pi/3 radians where pi radians is same as 180 degrees