Textbook Question
Write an expression that generates all angles coterminal with each angle. Let n represent any integer. 135°
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1. Measuring Angles
Coterminal Angles
Multiple Choice
Which of the following is a measure of an angle that is coterminal with ?
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Verified step by step guidance1
Understand that coterminal angles are angles that share the same initial and terminal sides when drawn in standard position. They differ by full rotations of 360 degrees.
To find angles coterminal with 135°, add or subtract multiples of 360° to 135°. The general formula is: \(\theta_{coterminal} = 135^\circ + 360^\circ \times k\), where \(k\) is any integer.
Calculate a few examples by substituting values for \(k\). For example, when \(k=1\), \(\theta = 135^\circ + 360^\circ = 495^\circ\); when \(k=-1\), \(\theta = 135^\circ - 360^\circ = -225^\circ\) (which is not in the options).
Compare the given options (495°, 45°, 90°, 225°) with the coterminal angles calculated. Identify which one fits the formula for coterminal angles.
Conclude that the angle from the options that is coterminal with 135° is the one that can be expressed as \(135^\circ + 360^\circ \times k\) for some integer \(k\).
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