Answer:
Explanation:
We can solve this equation for theta using the inverse cosine function, also known as the arccosine function, denoted as cos⁻¹. The arccosine function gives the angle whose cosine is a given value. In this case, we have:
cos theta = √3/2
Taking the inverse cosine of both sides, we get:
theta = cos⁻¹(√3/2)
Using a calculator or reference table, we can find that cos⁻¹(√3/2) = 30°. However, we need to consider the range of theta, which is given as 0 ≤ theta ≤ 360.
Since cos(theta) has a period of 360°, we can add or subtract multiples of 360° to theta without changing the value of cos(theta). Therefore, the solutions for theta are:
theta = 30° + 360°n, where n is an integer
theta = 360° - 30° + 360°n = 330° + 360°n, where n is an integer
These solutions satisfy the condition 0 ≤ theta ≤ 360. Therefore, the solutions for theta are:
theta = 30°, 390°
Note that 390° is equivalent to -30°, which is another solution to the equation. However, we excluded negative angles from the range of theta given in the problem, so we only include 30° as a solution.