Determine the XYcoordinates of the given point if the coordi

Determine the XY-coordinates of the given point if the coordinate axes are rotated through the indicated angle. (Round your answers to four decimal places.) (9,9), phi = 45degree (x, y) = (squareroot 2, 0)

Solution

(9,9) ---angle for this point : tan^-1(y/x) = tan^-1(9/9) = pi/4

So, further rotated through 45 deg: = pi/4 +pi/4 = pi/2

So, Point is now on y axis : y = sqrt(9^2+9^2) = 9sqrt(2)

So, point =( (9sqrt2 , 0)