Multiple Choice
If angle is in standard position and its terminal side lies along the positive -axis, what is its measure?
1. Measuring Angles
Angles in Standard Position
Multiple Choice
Given that angle is in standard position and its terminal side passes through the point on the coordinate plane, what is the degree measure of angle ? Round to the nearest whole degree.
A
degrees
B
degrees
C
degrees
D
degrees
Verified step by step guidance1
Identify the coordinates of the point through which the terminal side of angle BAC passes. Here, the point is (3, 4).
Recall that the angle in standard position is measured from the positive x-axis to the terminal side. To find this angle, we can use the tangent function, which relates the y-coordinate and x-coordinate of the point: \(\tan(\theta) = \frac{y}{x}\).
Substitute the coordinates into the tangent formula: \(\tan(\theta) = \frac{4}{3}\).
To find the angle \(\theta\), take the inverse tangent (arctangent) of \(\frac{4}{3}\): \(\theta = \tan^{-1}\left(\frac{4}{3}\right)\).
Use a calculator to find the value of \(\theta\) in degrees, then round to the nearest whole degree to get the measure of angle BAC.
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