Question

Find the measure of angle θ given θ' and the quadrant θ lies in.

Answer should be between 0 and 2π.
θ' = π/3; θ lies in Q3
θ = ?
A) π/3
B) 2π/3
C) 4π/3
D) 5π/3

Answer 1

To find the measure of angle θ given θ' and the quadrant θ lies in, we can use the co-function identity for sine and cosine. For the third quadrant, where θ lies, the sine function is negative. By substituting the given value and simplifying, we find that θ is equal to 4π/3.

Step-by-step explanation:

To find the measure of angle θ, we need to consider the given information. We are given that θ' (theta prime) equals π/3 and that θ lies in the third quadrant. In the third quadrant, the sine function is negative. Since θ' is positive, we can use the co-function identity for sine and cosine: sin(θ) = cos(π/2 - θ'). Substituting the given value, we get: sin(θ) = cos(π/2 - π/3). Simplifying this expression, we have: sin(θ) = cos(π/6). From the unit circle, we know that cos(π/6) = √3/2. Therefore, sin(θ) = √3/2. In the third quadrant, the sine function is negative. Hence, θ = 4π/3 (option C).