Question

For each of the following, determine an approximation for the angle & in radians (to three decimal places) when 0≤θ≤2π.

(a) cos(θ)= 1/3 and the terminal side of & is 3 in the second quadrant.
(b) cos(θ) = 2/3 and the terminal side of & is in the third quadrant.

Answer 1

To find an approximation for the angle & in radians, use the inverse cosine function.

Step-by-step explanation:

To determine an approximation for the angle & in radians, we can use the inverse cosine function. For part (a), since cos(&) = 1/3 and the terminal side of & is in the second quadrant, we can use the inverse cosine function to find &. We have ≈ cos-1(1/3) ≈ 1.230 radians.

For part (b), since cos(&) = 2/3 and the terminal side of & is in the third quadrant, we can again use the inverse cosine function to find &. We have ≈ cos-1(2/3) ≈ 0.841 radians.