Question

What are all the exact solutions of sin(x)=0? Give your answer in radians.

a) x=0
b) x=π/2​
c) x=π
d) x=π/2

Answer 1

The equation sin(x)=0 has solutions at x = nπ, where n is any integer. This includes 0 and π, representing the angles where the sine function intersects the horizontal axis on the unit circle.

Step-by-step explanation:

The exact solutions for sin(x)=0 occur when the angle x corresponds with the sine wave intersecting the horizontal axis. In terms of the unit circle, this happens when the angle's terminal side is on the x-axis. The sine function is zero at every integer multiple of π radians. Therefore, the equation sin(x)=0 has solutions at x = nπ, where n is any integer. This includes x=0 and x=π (i.e., 180 degrees), but not x=π/2 (i.e., 90 degrees) where the sine is 1.