How do I dertermine the measure of theta for the equation 4cos theta - sqrt 12 = 0. My answer was 2pi/3,4pi/3 I'm told it's wrong could you please show me how to do this type of question

Answer 1

4cos theta - √12 = 0
cos theta = 2√3/4 = √3/2

You should know by memory the ratio of sides of the 30-60-90 triangle
namely that cos 30º = √3/2
so theta is 30º or pi/6 radians

but the cosine is positive in quadrants I and IV.

We have the quadrant I angle, for the IVth one, take 360 - 30 = 300º or
2p - pi/6 = 11pi/6

You also should have memorized the 45-45-90 triangle which is √2 : √2 : 2,
and of course you must know the CAST rule to do these types of questions.