For an angle measured from the positive x-axis, the values of sin and cos are always which of the following?
A) less than -1
B) greater than or equal to -1 and less than or equal to 1
C) less than or equal to -1 or greater than or equal to 1
greater than or equal to −1 and less than or equal to 1
between -1 and +1
that is to the right (greater than) -1
and iis to the left (smaller than) +1
The correct answer is B) greater than or equal to -1 and less than or equal to 1.
The values of sine (sin) and cosine (cos) for an angle measured from the positive x-axis are always greater than or equal to -1 and less than or equal to 1, which corresponds to option B.
To understand why this is the case, we need to look at the unit circle, which is a circle centered at the origin with a radius of 1. When we measure an angle from the positive x-axis in a counterclockwise direction, we can capture the x-coordinate of the point where the angle intersects the unit circle as the cosine value, and the y-coordinate as the sine value.
Since the unit circle has a radius of 1, the coordinates of any point on the unit circle will have absolute values less than or equal to 1. As a result, the values of sin and cos for an angle measured from the positive x-axis, as represented by the points on the unit circle, will always fall within the range of -1 and 1.
Hence, option B, "greater than or equal to -1 and less than or equal to 1," is the correct answer.