Polar coordinates of a point are given. Find the rectangular coordinates of the point.
(-3, 120°)
(3, -135°)
First one
This is a little tricky.......r is always positive.....so....we need to add 180° to 120°
(-3, 120°) = ( 3, 300°)
So
cos 300 = x / 3
3cos300 = x
3 (1/2) = x
1.5 = x
And
sin300 = y / 3
3sin300 = y
3 * -√3/2 = y
-(3/2)√3 = y
-3√3 / 2 = y
So
(x , y ) = ( 1.5, -3√3 / 2 )
Second one
-135° = 360 - 135 = 225°
So...we have (3, 225°)
This one is easy.....it is a 45° angle in the 3rd Quadrant
The sine and cosine are equal here....so the x,y coordinates will be the same
cos 225 = x / 3
3cos 225 = x
3 ( -1 /√2) = x
-3/√2 = x = y
So
(x , y ) = ( -3/√2 , -3/√2 )