Question

How to find reference angle of 28pi/18

Answer 1

I'm a big fan of converting radians to degrees so the angles are easier to plot in a coordinate plane. Converting the radian measure to degrees is done with dimensional analysis, using the fact that there are 180 degrees in pi.
`(28\pi)/(18)=(14\pi)/(9)`. Let's reduce that first. Now that's out of the way...
`(14\pi)/(9)*(180)/(\pi) =280`. So 280 degrees. That angle will fall into the fourth quadrant, only 10 degrees "after" the negative y axis, which is 270. We go 10 degrees into the 4th quadrant. Reference angles are ALWAYS measured from the tip of the terminal ray of the angle to the nearest x axis. Since all 4 quadrants measure 90 degrees, 90 - 10 = 80. The reference angle, then, is 80 degrees. Converting that back to radians we get that the reference angle is
`(4\pi)/(9)`. There you go!