find all the values of theta, if theta is in the interval [0 degrees, 360 degrees) and has the given function value of cos theta: square root of 3 over 2

Question

 cos theta = square root of 3 over 2 

Answer 1

Hi Taylor,

cosθ = √3/2 The cosine of an angle is positive in the first quadrant and the fourth quadrant

In the first quadrant θ = cos^-1(√3/2 ) = 30° 

In the fourth quadrant θ= 360° - 30° =330°

The values of theta between 0°  and 360°  are 30°,330°  

Answer 2

Hi Taylor,

 

Recall from the unit circle that the cos 30° (cos π/6) is √3/2.

 

Cos is positive in the 1st and 4th quadrants.

 

So cos 330° will also be √3/2.