Would two coterminal angles for -13pi/6 be -25pi/6 and 11pi/6?
both yes.
To find coterminal angles for -13π/6, we need to add or subtract multiples of 2π (or 12π/6) until we obtain angles that differ from -13π/6.
First, let's add 12π/6 (or 2π) to -13π/6:
-13π/6 + 12π/6 = -π/6
The angle -π/6 is coterminal with -13π/6.
Next, let's subtract 12π/6 (or 2π) from -13π/6:
-13π/6 - 12π/6 = -25π/6
Therefore, -25π/6 is another coterminal angle of -13π/6.
So, the two coterminal angles for -13π/6 are -π/6 and -25π/6.
The angle 11π/6 is not coterminal with -13π/6.
Yes, you are correct! The angles -25π/6 and 11π/6 are indeed coterminal angles for -13π/6.
To find coterminal angles, all you need to do is add or subtract integer multiples of 2π (or 360 degrees) to the given angle. This can be done because adding or subtracting a full revolution (360 degrees or 2π) results in an angle that holds the same position on the unit circle.
For -13π/6, you can add 2π to get a larger angle: -13π/6 + 2π = -13π/6 + 12π/6 = -π/6.
Alternatively, you can subtract 2π to get a smaller angle: -13π/6 - 2π = -13π/6 - 12π/6 = -25π/6.
Both -π/6 and -25π/6 are coterminal angles for -13π/6.
Similarly, if you add 2π to -13π/6, you will get another coterminal angle: -13π/6 + 2π = -13π/6 + 12π/6 = 11π/6.
So, -25π/6 and 11π/6 are coterminal angles for -13π/6.