Question 1174873: For each of the following, there are two points on the unit circle that fit the given description. Without finding theta, describe how the two points are related to each other.
a) cos theta = -0.4540
b) sin theta = 0.6820
c) tan theta = -1.280
Answer by greenestamps(13206)   (Show Source):
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a) cos theta = -0.4540
On the unit circle, cosine is the x value.
There are two points on the unit circle with x = -0.4540.
The y values of those two points are opposites -- one positive and one negative.
The relationship of the two points is that they are mirror images of each other with respect to the x-axis.
b) sin theta = 0.6820
On the unit circle, sine is the y value.
There are two points on the unit circle with y = 0.6820.
The x values of those two points are opposites -- one positive and one negative.
The relationship of the two points is that they are mirror images of each other with respect to the y-axis.
c) tan theta = -1.280
On the unit circle, tangent is the ratio of sine and cosine, or y/x.
There are two points on the unit circle with y/x = -1.280.
One has y positive and x negative (quadrant II); the other has y negative and x positive (quadrant IV).
For both points, the absolute values of both x and y are the same. That means the two points are images of each other with respect to the origin.
Another way of describing that would be to say the two points are endpoints of a diameter of the unit circle, or by saying that the two points are 180 degrees apart on the unit circle.
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