Question

Solve 2√3costheta=3​

Answer 1

see explanation

Explanation:

Given

2
`√(3)` cosΘ = 3 ( divide both sides by 2
`√(3)` )

cosΘ =
`(3)/(2√(3) )` =
`(3√(3) )/(6)` =
`(√(3) )/(2)` , thus

Θ =
`cos^(-1)` (
`(√(3) )/(2)` ) = 30°

Since cosΘ > 0 then Θ in first/ fourth quadrants

This Θ = 360° - 30° = 330°

Solution Θ = 30°, 330° for 0 < Θ < 360

Answer 2

pi/6, 11pi/6

Explanation:

so first we divide both sides by 2root 3

we then get cos theta = 3/2root3

do some rationalizing, it turns to cos theta = root 3/2

from here we take the cosine inverse of root3/2 to get our basic angle (pi/6)

from here we want where cos theta is positive, using the CAST circle or ASTC circle, from top right to bottom right, we find that cos theta is positive at theta, 2pi - theta

Now you haven't given a domain, so ill assume [0,2pi]

which means you have cos theta = theta, 2pi - theta

therefore = pi/6, 2pi - pi/6

which simplifies to = pi/6, 11pi/6