Question

Find all solutions to the equation. 4 = 5 2 cos 0+1=0 6 Write your answer in radians in terms of it, and use the "or" button as necessary. Example: 0 = 5 +2ka, k€ Z or 0 = 5+ka, kė Z

Answer 1

To find the solutions to the equation 4 = 5 + 2cos(θ) + 1 = 0, rearrange the equation to isolate the cosine term. The solutions can be found by considering the unit circle, where the x-coordinate of a point on the unit circle represents the cosine value of the angle formed with the positive x-axis. The angles for which cos(θ) = -1/2 can be found at π/3 and 5π/3 in the unit circle. Therefore, the solutions to the equation are θ = π/3 + 2kπ and θ = 5π/3 + 2kπ, where k is an integer.

Step-by-step explanation:

To find the solutions to the equation 4 = 5 + 2cos(θ) + 1 = 0, we can start by rearranging the equation to isolate the cosine term. Subtracting 5 from both sides, we get -1 = 2cos(θ). Dividing both sides by 2, we have -1/2 = cos(θ).

The solutions to this equation can be found by considering the unit circle, where the x-coordinate of a point on the unit circle represents the cosine value of the angle formed with the positive b

The angles for which cos(θ) = -1/2 can be found at π/3 and 5π/3 in the unit circle. Therefore, the solutions to the equation are θ = π/3 + 2kπ and θ = 5π/3 + 2kπ, where k is an integer.

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