Question

What values for theta(0 <= theta <= 2pi) satisfy the equation?

2 sin theta cos theta + sqrt 3 cos theta = 0

a. pi/2, 4pi/3, 3pi/2, 5pi/3
b. pi/2, 3pi/4, 3pi/2, 5pi/3
c. pi/2, 3pi/4, 3pi/2, 5pi/4
d. pi/2, pi/4, 3pi/2, 5pi/3

Answer 1

2 sin t cos t + √3 cos t = 0
cos t ( 2 sin t + √3 ) = 0
Therefore:
cos t = 0, t 1 = π/2, t 2 = 3 π/2
or:
2 sin t + √3 = 0
2 sin t = - √3
sin t = - √3 / 2
t 3 = 4 π/3, t 4 = 5 π/3
Answer:
a ) π/2, 4π/3, 3π/2. 5π/3.