How do I find 1 positive and 1 negative coterminal angle for:
1) -460 degrees
2) 11pi/4
3) -12pi/5
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To find coterminal angles, you can follow these steps:
1) For a given angle, add or subtract multiples of 360 degrees (or multiples of 2π radians) until you get a positive and a negative angle. These new angles will be coterminal with the given angle.
Let's apply these steps to each of the angles you mentioned:
1) -460 degrees:
To find the positive coterminal angle, add 360 degrees to -460:
-460 + 360 = -100 degrees
To find the negative coterminal angle, subtract 360 degrees from -460:
-460 - 360 = -820 degrees
So, the positive coterminal angle for -460 degrees is -100 degrees, and the negative coterminal angle is -820 degrees.
2) 11pi/4:
To find the positive coterminal angle, add 2π radians (or 360 degrees) to 11π/4:
11π/4 + 2π = 11π/4 + 8π/4 = 19π/4
To find the negative coterminal angle, subtract 2π radians (or 360 degrees) from 11π/4:
11π/4 - 2π = 11π/4 - 8π/4 = 3π/4
So, the positive coterminal angle for 11π/4 is 19π/4, and the negative coterminal angle is 3π/4.
3) -12π/5:
To find the positive coterminal angle, add 2π radians (or 360 degrees) to -12π/5:
-12π/5 + 2π = -12π/5 + 10π/5 = -2π/5
To find the negative coterminal angle, subtract 2π radians (or 360 degrees) from -12π/5:
-12π/5 - 2π = -12π/5 - 10π/5 = -22π/5
So, the positive coterminal angle for -12π/5 is -2π/5, and the negative coterminal angle is -22π/5.
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