Evaluate θ for cos θ = -√3/2 if it is between 0 and 2π. How would one do this?

Question

Please help I do not understand this question.:c

Answer 1

cosine < 0 so it's in quadrant II or III.

the 1-sqr3- 2 right triangle is a 30-60-90 degree triangle

theta is 180 degrees + or - 60 degrees = 240 degrees or 120 degrees

theta = 2pi/3 or 4pi/3

cosine is the adjacent side over hypotenuse = -sqr3/2

You could just plug that into a calculator with trig functions and use the inverse cosine function to find theta

Or, you may just recognize this is a common 30- 60 - 90 triangle when you graph it on a unit circle.