Multiple Choice
Which of the following best describes the terminal side of an angle in standard position?
1. Measuring Angles
Angles in Standard Position
Multiple Choice
An angle in standard position has its terminal side passing through the point on the unit circle. Estimate the measure of this angle to the nearest one-half radian.
A
radians
B
radians
C
radians
D
radians
Verified step by step guidance1
Identify the coordinates of the point on the unit circle, which are given as (0, -1). Since the point lies on the unit circle, its coordinates correspond to (cos(\(\theta\)), sin(\(\theta\))) for some angle \(\theta\) in standard position.
Recognize that the x-coordinate is 0 and the y-coordinate is -1, so we have \(\cos\)(\(\theta\)) = 0 and \(\sin\)(\(\theta\)) = -1.
Recall the unit circle values where \(\sin\)(\(\theta\)) = -1 occurs. This happens at the angle where the terminal side points straight down along the negative y-axis.
Determine the angle \(\theta\) in radians that corresponds to this point. On the unit circle, the angle with \(\sin\)(\(\theta\)) = -1 and \(\cos\)(\(\theta\)) = 0 is \(\theta\) = \(\frac{3\pi}{2}\) radians.
Convert \(\frac{3\pi}{2}\) radians to a decimal approximation to estimate the angle measure to the nearest one-half radian.
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