![]() ![]() For example, one revolution for our exemplary α is not enough to have both a positive and negative coterminal angle – we'll get two positive ones, 1040 ° 1040\degree 1040° and 1760 ° 1760\degree 1760°. The number or revolutions must be large enough to change the sign when adding/subtracting. For our previously chosen angle, α = 1400 ° \alpha = 1400\degree α = 1400°, let's add and subtract 10 10 10 revolutions (or 100 100 100, why not): Other negative coterminal angles are − 40 ° -40\degree − 40°, − 400 ° -400\degree − 400°, − 760 ° -760\degree − 760°.Īlso, you can simply add and subtract a number of revolutions if all you need is any positive and negative coterminal angle. ( 2 π 2\pi 2 π, 4 π 4\pi 4 π, 6 π 6\pi 6 π.), to obtain positive or negative coterminal angles to your given angle.įor example, if α = 1400 ° \alpha = 1400\degree α = 1400°, then the coterminal angle in the [ 0, 360 ° ) [0,360\degree) [ 0, 360° ) range is 320 ° 320\degree 320° – which is already one example of a positive coterminal angle. ![]() One method is to find the coterminal angle in the 0 ° 0\degree 0° and 360 ° 360\degree 360° range (or [ 0, 2 π ) [0,2\pi) [ 0, 2 π ) range), as we did in the previous paragraph (if your angle is already in that range, you don't need to do this step). ![]() If you want to find a few positive and negative coterminal angles, you need to subtract or add a number of complete circles. ![]()
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