Question

Find the exact value of the trigonometric function at the given real number: sin7π/6

a)−1/2
b)−√3/2
c)3/2
d)1/2

Answer 1

The exact value of the sine of 7π/6 is -1/2, as this angle is in the third quadrant where sine values are negative.

Step-by-step explanation:

To find the exact value of the trigonometric function sin(7π/6), we first recognize that 7π/6 is an angle located in the third quadrant where sine is negative.

The reference angle for 7π/6 is π/6. In the unit circle, sin(π/6) equals 1/2, but since sine is negative in the third quadrant, sin(7π/6) equals -1/2.

Therefore, the exact value of sin(7π/6) is -1/2, which corresponds to option (a).