Question

find all values of θ, if θ is in the interval 0,360°) and has the given function value.

cos(θ)=\frac{\sqrt{3}}{2}

a. 45° and 225°
b. 135° and 225°
c. 30° and 330°
d. 225° and 315°

Explanation:

Step1: Recall the reference angle

We know that \(\cos(30^{\circ})=\frac{\sqrt{3}}{2}\). The reference angle \(\theta_{ref} = 30^{\circ}\).

Step2: Determine the quadrants

Cosine is positive in the first and fourth quadrants.

• For the first - quadrant: \(\theta=\theta_{ref}\). So \(\theta = 30^{\circ}\).
• For the fourth - quadrant: \(\theta = 360^{\circ}-\theta_{ref}\). Substitute \(\theta_{ref}=30^{\circ}\), we get \(\theta=360^{\circ}- 30^{\circ}=330^{\circ}\)

Answer:

C. \(30^{\circ}\) and \(330^{\circ}\)