Question

Which of the following sets of angle measures is equivalent to

Answer 1

The angles are 150 degrees and 210 degrees

EXPLANATION :

Recall the cosine of 30 degrees.

`\cos30=(√(3))/(2)`

From the problem, we need to find the measurement of the angle that will give a cosine value of :

`\cos^(-1)(-(√(3))/(2))`

Negative values of cosines occur in the Second and Third Quadrant.

Reference angles are always on the x-axis.

Since we know that cos 30 is √3/2, then the value of the angles is 30 degrees.

The first angle must be subtracted from 180 degrees as shown above.

That's 180 - 30 = 150

The second angle must be added to 180 degrees as also shown above.

That's 180 + 30 = 210