Multiple Choice
If is an angle in standard position whose initial side is along the positive x-axis and whose terminal side passes through the point , what is the measure of in degrees?
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1. Measuring Angles
Angles in Standard Position
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Which of the following angles is coterminal with in standard position?
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Verified step by step guidance1
Recall that two angles are coterminal if they differ by a full rotation, which is 360 degrees. This means that if you add or subtract 360 degrees from an angle, the resulting angle will be coterminal with the original angle.
Start with the given angle, which is 45 degrees. To find angles coterminal with 45 degrees, add or subtract multiples of 360 degrees: \$45^\circ + 360^\circ = 405^\circ\( and \)45^\circ - 360^\circ = -315^\circ$.
Check each of the given options to see if they can be expressed as \$45^\circ \pm 360^\circ k\( for some integer \)k$. The options are 90°, 180°, 405°, and 135°.
Compare each option to 45° plus or minus multiples of 360°. Notice that 405° equals \$45^\circ + 360^\circ$, so it is coterminal with 45°.
Conclude that the angle 405° is coterminal with 45° because it represents the same terminal side after one full rotation plus the original 45°.
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