Final answer:
To solve cos²θ = 3/4 for 0° < θ < 360°, we find that θ equals 30° and, due to the symmetry of the cosine function, also 330°, by considering the related angle in the fourth quadrant.
Step-by-step explanation:
To solve for θ in the range 0° < θ < 360° where cos²θ = 3/4, we first take the square root of both sides of the equation. This gives us cosθ = ±√(3/4). Knowing that the cosine function is positive in the first and fourth quadrants, and given the range, we can find the principal and related acute angles.
Since the square root of 3/4 is equal to √3/2, we are looking for angles whose cosine is √3/2 or -√3/2. Remembering that the cosine of 30° is equal to √3/2, we find θ=30° for the principal angle. However, since we also have the negative solution -√3/2, we need to find the angle that has this cosine value in the fourth quadrant. The related acute angle is still 30°, but the angle in the fourth quadrant is 360° - 30°, which is 330°.
Therefore, the solutions are θ = 30° and θ = 330°.