What point on the unit circle corresponds to -5pi/4?
A. (-Root2/2, Root2/2)
B.(-Root3/2, 1/3
C.(-1/2, Root3/2)
D.(0,1)
D?
45º reference angle in quad II
looks like A
To determine the point on the unit circle corresponding to -5π/4, you can use the properties of the unit circle and trigonometry.
First, let's break down the angle -5π/4. The value -5π/4 represents a rotation of the angle -π/4, clockwise direction.
When dealing with the unit circle, it's helpful to use the reference angle, which is the positive angle between the terminal side of the given angle and the x-axis. The reference angle for -π/4 is π/4.
Now, consider the coordinates on the unit circle. The x-coordinate represents the cosine value, and the y-coordinate represents the sine value.
Since the reference angle is π/4, we know that the cosine of π/4 is equal to the sine of π/4, which is √2/2. Thus, the x-coordinate is √2/2.
However, since the angle is in the 4th quadrant (clockwise), the x-coordinate will be negative.
Therefore, the point on the unit circle corresponding to -5π/4 is (-√2/2, y), where y is the y-coordinate.
Now, let's look at the options provided:
A. (-√2/2, √2/2) - This is correct for the angle π/4, not -5π/4.
B. (-√3/2, 1/3) - This option is not correct.
C. (-1/2, √3/2) - This option is not correct.
D. (0, 1) - This option is not correct.
Therefore, the correct answer is not D.