The coordinates of each point are listed below:
- P(x, y) = (- cos θ, - sin θ)
- P(x, y) = (sin θ, - cos θ)
- P(x, y) = (- cos θ, - sin θ)
- P(x, y) = (- sin θ, - cos θ)
What points of the unit circle are related to a given set of angles?
In this question we have a point P with coordinates (x, y) = (cos θ, sin θ), where θ is the angle the segment OP in standard position. To determine the sine and the cosine of the sum of two angles, we can make use of the following trigonometric formulas:
cos (θ ± α) = cos θ · cos α ∓ sin θ · sin α (1)
sin (θ ± α) = sin θ · cos α ± cos θ · sin α (2)
Then, we proceed to find the location of each point:
Case 1: cos (π + θ) = cos π · cos θ - sin π · sin θ = - cos θ, sin (π + θ) = sin π · cos θ + cos π · sin θ = - sin θ : P(x, y) = (- cos θ, - sin θ)
Case 2: cos (θ - 0.5π) = cos θ · cos 0.5π + sin θ · sin 0.5π = sin θ, sin (θ - 0.5π) = sin θ · cos 0.5π - cos θ · sin 0.5π = - cos θ : P(x, y) = (sin θ, - cos θ)
Case 3: cos (2π - θ) = cos 2π · cos θ + sin 2π · sin θ = - cos θ, sin (2π - θ) = sin 2π · cos θ - cos 2π · sin θ = - sin θ : P(x, y) = (- cos θ, - sin θ)
Case 4: cos (1.5π - θ) = cos 1.5π · cos θ + sin 1.5 π · sin θ = - sin θ, sin (1.5π - θ) = sin 1.5π · cos θ - cos 1.5π · sin θ = - cos θ : P(x, y) = (- sin θ, - cos θ)
To learn more on trigonometric functions: https://brainly.com/question/14434745
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