Find both the radian and degree measure of the angle between the point on the coordinate plane and x-axis without the use of a calculator.

Question

Find both the radian and degree measure of the angle between the point on the coordinate plane and x-axis without the use of a calculator. Show and explain your work.

Answer 1

with a point (x,y) and a line from the origin (0,0) to the point (x,y),

the angle formed with the x axis is: tan^-1(y/x)

for example if x=y then the angle = 45 degrees or pi/4 radians

if y/x = sqr3, then the angle = 60 degrees or pi/3 radians

if y>0 and x=0, then the angle = 90 degrees or pi/2 radians. the tangent of 90 degrees is undefined.

y/0 is undefined