(C) sin(-r) = -a
(D) sin(r) = -a
Explanation:
The unit circle definition allows us to extend the domain of sine and cosine to all real numbers. The process for determining the sine/cosine of any angle θ is as follows:
Starting from (1,0) move along the unit circle in the counterclockwise direction until the angle that is formed between your position, the origin, and the positive x-axis is equal to θ.
In the question, sin(-r) = -a and sin(r) = -a is equal to the x-coordinate, thus they are not correct.
An image is attached for reference.
The incorrect statements are:
Consider any angle [tex]\theta[/tex] in standard position together with a unit circle. The terminal side will intersect the circle at some point (x, y) .
Let the unit circle moves in the counterclockwise direction until the angle that is formed between our position, the origin, and the positive x-axis is equal to θ.
The y-coordinate of this point is always equal to the sine of the angle, and the x-coordinate of this point is always equal to the cosine of the angle.
That is
sin θ= y
cosθ = x
Now, we have point (a, b) be on a unit circle.
If (a, b) has a rotation of r degrees.
Then
sin(-r) = -a,
sin(r) = -a is equal to the x-coordinate.
Therefore they are incorrect.
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