Solve the following equation for 0 ≤ ѳ< π
cos ѳ= 1/2
choices:
A) {pie/3}
B) {-3pie/4, 3pie/4}
C) {-pie/4, pie/4}
D) {pie/4, 3pie/4, 5pie/4, 7pie/4}
SHOW YOUR WORK/STEPS
To solve the equation cos ѳ = 1/2, we need to find the angles between 0 and π where cosine is equal to 1/2.
The value of cosine is positive in the first and fourth quadrants. In the first quadrant, the reference angle where cosine is 1/2 is π/3. In the fourth quadrant, the reference angle is 2π/3.
Therefore, the solutions for 0 ≤ ѳ < π are:
ѳ = π/3 (in the first quadrant)
ѳ = 5π/3 (in the fourth quadrant)
However, we can eliminate 5π/3 since it is outside the given range.
So, the correct answer is:
A) {π/3}