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To find a coterminal angle, you can subtract or add multiples of 360 degrees. For the angle 534 degrees, you can subtract 360 degrees: 534 - 360 = 174 degrees. Therefore, the coterminal angle of 534 degrees is 174 degrees.
To find an angle that is coterminal with -40 degrees, you can add or subtract multiples of 360 degrees. In this case, adding 360 degrees gives you 320 degrees, which is coterminal with -40 degrees. Therefore, the angle that is coterminal with -40 degrees is 320 degrees.
To find the greatest negative coterminal angle of 122 degrees, subtract 360 degrees until the angle is negative. Starting with 122 degrees, subtracting 360 gives -238 degrees. Since -238 degrees is less than -360 degrees, it is the greatest negative coterminal angle for 122 degrees.
To find a coterminal angle for 41 degrees, you can add or subtract multiples of 360 degrees. For example, subtracting 360 degrees gives you a coterminal angle of 41 - 360 = -319 degrees. Alternatively, adding 360 degrees results in 41 + 360 = 401 degrees. Therefore, -319 degrees and 401 degrees are both coterminal with 41 degrees.
To find a positive angle less than 360 degrees that is coterminal with 390 degrees, subtract 360 degrees from 390 degrees. This gives you 390 - 360 = 30 degrees. Therefore, the positive angle that is coterminal with 390 degrees and less than 360 degrees is 30 degrees.
To find a coterminal angle, you can subtract or add multiples of 360 degrees. For the angle 534 degrees, you can subtract 360 degrees: 534 - 360 = 174 degrees. Therefore, the coterminal angle of 534 degrees is 174 degrees.
To find an angle that is coterminal with -40 degrees, you can add or subtract multiples of 360 degrees. In this case, adding 360 degrees gives you 320 degrees, which is coterminal with -40 degrees. Therefore, the angle that is coterminal with -40 degrees is 320 degrees.
To find the greatest negative coterminal angle of 122 degrees, subtract 360 degrees until the angle is negative. Starting with 122 degrees, subtracting 360 gives -238 degrees. Since -238 degrees is less than -360 degrees, it is the greatest negative coterminal angle for 122 degrees.
To find negative coterminal angles, subtract 360 degrees from the given angles. For 25 degrees, the negative coterminal angle is (25 - 360 = -335) degrees. For 150 degrees, it is (150 - 360 = -210) degrees. For 300 degrees, the negative coterminal angle is (300 - 360 = -60) degrees.
To find a coterminal angle for 41 degrees, you can add or subtract multiples of 360 degrees. For example, subtracting 360 degrees gives you a coterminal angle of 41 - 360 = -319 degrees. Alternatively, adding 360 degrees results in 41 + 360 = 401 degrees. Therefore, -319 degrees and 401 degrees are both coterminal with 41 degrees.
To find a positive angle less than 360 degrees that is coterminal with 390 degrees, subtract 360 degrees from 390 degrees. This gives you 390 - 360 = 30 degrees. Therefore, the positive angle that is coterminal with 390 degrees and less than 360 degrees is 30 degrees.
To find an angle that is coterminal with 135 degrees, you can add or subtract multiples of 360 degrees. For example, adding 360 degrees gives you 495 degrees (135 + 360). Alternatively, subtracting 360 degrees results in -225 degrees (135 - 360). Both 495 degrees and -225 degrees are coterminal with 135 degrees.
To find the least positive angle coterminal with ( \frac{\pi}{6} ), you can add or subtract multiples of ( 2\pi ). Since ( \frac{\pi}{6} ) is already a positive angle and less than ( 2\pi ), it is the least positive angle coterminal with itself. Therefore, the least positive angle coterminal with ( \frac{\pi}{6} ) is ( \frac{\pi}{6} ).
There are an infinite number of angles that are coterminal with a given angle because coterminal angles differ by full rotations. Specifically, for any angle ( \theta ), you can find coterminal angles by adding or subtracting multiples of ( 360^\circ ) (or ( 2\pi ) radians). This means that ( \theta + 360^\circ n ) (where ( n ) is any integer) will always result in an angle that shares the same terminal side as ( \theta ), leading to an infinite set of such angles.
Coterminal angles are angles that are formed at the same vertex.
To find an angle that is coterminal with ( \frac{3\pi}{2} ), you can add or subtract multiples of ( 2\pi ). For example, ( \frac{3\pi}{2} + 2\pi = \frac{3\pi}{2} + \frac{4\pi}{2} = \frac{7\pi}{2} ) is coterminal with ( \frac{3\pi}{2} ). Similarly, subtracting ( 2\pi ) gives ( \frac{3\pi}{2} - 2\pi = \frac{3\pi}{2} - \frac{4\pi}{2} = -\frac{\pi}{2} ), which is also coterminal.
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