Question

(4, 6) counterclockwise

Answer 1

To rotate the point (4, 6) counterclockwise, you can use the following rotation formula:

x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)

Since we want to rotate counterclockwise, we can use a positive angle theta. Let's say we want to rotate by 30 degrees.

theta = 30 degrees

Converting theta to radians:
theta(radians) = theta(degrees) * pi / 180
= 30 * pi / 180
= pi / 6 radians

Using the rotation formula:

x' = 4*cos(pi/6) - 6*sin(pi/6)
= 4*(√3/2) - 6*(1/2)
= 2√3 - 3

y' = 4*sin(pi/6) + 6*cos(pi/6)
= 4*(1/2) + 6*(√3/2)
= 2 + 3√3

Therefore, after rotating the point (4, 6) counterclockwise by 30 degrees, the new coordinates are approximately (2√3 -3, 2 + 3√3).