Multiple Choice
Which of the following best describes an angle in standard position in the coordinate plane?
1. Measuring Angles
Angles in Standard Position
Multiple Choice
If an angle is in standard position and its terminal side passes through the point on the coordinate plane, what is the measure of the angle in degrees?
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Verified step by step guidance1
Identify that the angle in standard position has its vertex at the origin (0,0) and its terminal side passes through the point (1,1).
Recall that the measure of the angle \( \theta \) can be found using the tangent function, since \( \tan(\theta) = \frac{y}{x} \) for a point \((x,y)\) on the terminal side.
Calculate \( \tan(\theta) = \frac{1}{1} = 1 \).
Use the inverse tangent function to find the angle: \( \theta = \tan^{-1}(1) \).
Recognize that \( \tan^{-1}(1) \) corresponds to an angle of 45 degrees in the first quadrant, so the measure of the angle is \( 45^\circ \).
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