Question #d5424

1 Answer
Feb 15, 2018

#pi/2#

Please see below for explanation..

Explanation:

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The following figure shows an example of coterminal angles and their definition.

enter image source here

As you can see, the initial side of the angles are on the positive side of the #x#-axis. Both angles start from the #x#-axis and if the angle is positive it opens counterclockwise. If it is negative it opens clockwise.

They are called coterminal because they share the terminal sides together. In this example #570^@# and #-150^@# are coterminal.

We can write #(-15pi)/2# as follows:

#(-15pi)/2=-(14pi)/2-pi/2=-7pi-pi/2#

To figure out where the terminal side of this angle will be, we have to consider that when we start at the positive side of the #x#-axis and move clockwise (because it is a negative angle), every time we go full circle and end up at our starting point, we have gone #-2pi# radians.

Therefore, if we go around #3# times we will have gone #6pi# radians at which time we are back where we started. Now, if we go half a circle more we will end up on the negative side of the #x#-axis. This takes care of the #-7pi# part.

We then continue another #-pi/2# which will put our terminal side on the positive side of the #y#-axis.

The angle that is between #0# and #2pi# and is coterminal with #(-15pi)/2#, starts from the positive side of the #x#-axis and goes counterclockwise (because it is a positive angle) and ends up at the positive side of the #y#-axis. This angle would be #pi/2.#