Multiple Choice
If an angle in standard position has its terminal side passing through the point on the coordinate plane, what is the measure of angle to the nearest degree?
1. Measuring Angles
Angles in Standard Position
Multiple Choice
If an angle in standard position has its terminal side passing through the point , which of the following could be the measure in degrees of the angle's reference angle ?
A
B
C
D
Verified step by step guidance1
Identify the quadrant in which the terminal side of the angle lies by examining the coordinates of the point (-3, 4). Since x is negative and y is positive, the point is in the second quadrant.
Recall that the reference angle is the acute angle formed between the terminal side of the angle and the x-axis. In the second quadrant, the reference angle \( m \) can be found by subtracting the angle from 180°.
Calculate the angle \( \theta \) formed by the terminal side using the coordinates. First, find the tangent of the angle using \( \tan(\theta) = \frac{|y|}{|x|} = \frac{4}{3} \).
Find the angle \( \alpha \) whose tangent is \( \frac{4}{3} \) using the inverse tangent function: \( \alpha = \tan^{-1}\left(\frac{4}{3}\right) \). This angle \( \alpha \) is the reference angle \( m \) because it is the acute angle between the terminal side and the x-axis.
Use the reference angle \( m = \alpha \) to check which of the given options matches this value or is consistent with the quadrant and reference angle definition.
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