Question

List three angles (in radian measure) that have a sine of -1/2.

a) π/6, 7π/6, 11π/6
b) π/4, 3π/4, 5π/4
c) π/3, 2π/3, 4π/3
d) π/2, π, 3π/2

Answer 1

The angles in radian measure that have a sine of -1/2 specifically are π/2, π, and 3π/2, as they correspond to the correct quadrants and reference angles on the unit circle.

Step-by-step explanation:

π/2, π, 3π/2. Sine has a value of -1/2 at specific angles in the unit circle. These angles correspond to the locations on the unit circle where the y-coordinate (which represents the sine value) is -1/2.

Since sine is positive in the first and second quadrants and negative in the third and fourth quadrants, we need to find angles in the third and fourth quadrants where sine is -1/2. The reference angle with a sine of 1/2 is π/6 radians. The corresponding angles in the third and fourth quadrants are 7π/6 and 11π/6 respectively. However, the angles provided in the options are not all in radian measure, and not all correspond to a sine of -1/2.