Question

When you subtract an angle θ from

3/2 π, what is the equivalent of the sine of this new angle?
a) The cosine of θ
b) Negative cosine of θ
c) The sine of θ
d) Negative sine of θ

Answer 1

When subtracting an angle θ from 3/2 π, the equivalent of the sine of the new angle will be the sine of the reference angle in the first or second quadrant, and negative sine of the reference angle in the third or fourth quadrant.

Step-by-step explanation:

When subtracting an angle θ from 3/2 π, the new angle is equal to 3/2 π - θ. To find the equivalent of the sine of this new angle, we need to use the reference angle. The reference angle is the angle formed when dropping a perpendicular line from the endpoint of the new angle to the x-axis. Since the original angle is expressed in terms of π, we can use the unit circle to find the sine of the reference angle.

The reference angle will be positive if the new angle is in the first or second quadrant, and negative if the new angle is in the third or fourth quadrant.

If the new angle is in the first or second quadrant, the equivalent of the sine of the new angle will be the sine of the reference angle. If the new angle is in the third or fourth quadrant, the equivalent of the sine of the new angle will be the negative sine of the reference angle.