Question

The measure of angle 0 is 3pi/2. the measure of its reference angle is pi/blank, and tan 0 is blank

Answer 1

For θ = 3π/2 radians, the reference angle is π/2, and tan θ is undefined because the tangent function involves division by zero at that angle.

Step-by-step explanation:

The measure of angle θ is 3π/2 radians. A reference angle is the acute angle formed by the x-axis and the terminal side of the given angle when it is in standard position. Since 3π/2 radians places the angle in the third quadrant where the angle's terminal side coincides with the y-axis, the reference angle here is π/2 radians, which is 90 degrees. The tangent of an angle is the ratio of the y-coordinate to the x-coordinate of a point on the unit circle at that angle. However, at 3π/2 radians, the tangent function is undefined because the x-coordinate is 0, and division by zero is not possible in mathematics. Thus, tan θ is undefined.

Answer 2

If the measure of angle 0 is 3π/2, then the measure of its reference angle is π/2. This is because the reference angle is the acute angle formed by the terminal of the given angle and the x-axis. That is why the position of the terminal angle is 270° and between that and the x-axis is 90°.