For the following values of t find (a) the reference number of t and (B) the terminal point determined by t

Question

-11 pie/6

Answer 1

To find the reference number of -11pi/6, we need to find the equivalent angle within one revolution (2pi) that has the same terminal side.

To do this, we can add or subtract multiples of 2pi until we get an angle between 0 and 2pi.

In this case, we can add 2pi to -11pi/6 repeatedly until we get a value within the range of 0 to 2pi.

(-11pi/6) + (12pi/6) = pi/6

Thus, the reference number of -11pi/6 is pi/6.

To find the terminal point determined by -11pi/6, we can use the unit circle.

Starting from the positive x-axis (the reference angle of 0), we can count counter-clockwise by adding the angle -11pi/6 to the reference angle.

pi/6 + (-11pi/6) = -10pi/6

The terminal point determined by -11pi/6 is on the negative x-axis, specifically (-1, 0).