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Multiple Choice
Find the sine, cosine, and tangent of each angle using the unit circle. θ=225°,(−22,−22)
A
sinθ=−22,cosθ=−22,tanθ=2
B
sinθ=22,cosθ=−22,tanθ=−1
C
sinθ=−22,cosθ=−22,tanθ=1
D
sinθ=22,cosθ=22,tanθ=12
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1
The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. Each point on the unit circle corresponds to an angle θ measured from the positive x-axis.
For an angle θ = 225°, we are in the third quadrant of the unit circle. In this quadrant, both sine and cosine values are negative.
The coordinates of the point on the unit circle corresponding to θ = 225° are given as (-√2/2, -√2/2). These coordinates represent (cosθ, sinθ).
Therefore, for θ = 225°, we have cosθ = -√2/2 and sinθ = -√2/2.
The tangent of an angle θ is given by tanθ = sinθ/cosθ. Substituting the values, we get tanθ = (-√2/2) / (-√2/2) = 1.