Question

Use a reference angle to write sin(31π36) in terms of the sine of a positive acute angle. include parentheses in your answer

A) sin(π/36)
B) sin(5π/36)
C) sin(11π/36)
D) sin(13π/36)

Answer 1

Using the reference angle concept, sin(31π/36) can be written as sin(5π/36), which is the positive acute reference angle in the second quadrant.

Step-by-step explanation:

To find the sine of π - θ, we use the fact that sin(π - θ) = sin θ. Since the reference angle for π - θ lies in the second quadrant, where sine is positive, we can directly use the reference angle to find the equivalent sine expression.

For sin(31π/36), we subtract this from π to find its reference angle:

π - 31π/36 = 36π/36 - 31π/36 = 5π/36

Therefore, sin(31π/36) is equivalent to sin(5π/36), as this positive acute angle is the reference angle for 31π/36.