For which value of is tan theta equal to sin theta (point) x/2; pi/3; (3pi)/2

Answer 1

For the given condition, tan(theta) = sin(theta), we can use the trigonometric identities to solve for the value of theta.

Given:
tan(theta) = sin(theta)
tan(theta) - sin(theta) = 0
sin(theta)/cos(theta) - sin(theta) = 0 (Using the definition of tan in terms of sin and cos)
sin(theta)(1/cos(theta) - 1) = 0
sin(theta)(1 - cos(theta))/(cos(theta)) = 0

For sin(theta) to be equal to 0, theta must be equal to 0, pi, 2pi, etc. But for cos(theta) to not be equal to 0, we must look for a different solution.

1 - cos(theta) = 0
cos(theta) = 1
theta = 0

Therefore, the value of theta is 0 radians.