Question

(2,2) rotated 136 degrees clockwise

Answer 1

To rotate a point (x, y) by an angle θ clockwise about the origin, the new coordinates (x', y') can be found using the following formulas:

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

In this case, we want to rotate the point (2, 2) by 136 degrees clockwise. Converting 136 degrees to radians:

θ = 136 degrees * π / 180 ≈ 2.37365 radians

Substituting the values into the formulas:

x' = 2 * cos(2.37365) - 2 * sin(2.37365)
y' = 2 * sin(2.37365) + 2 * cos(2.37365)

Using a calculator, we can find:

x' ≈ -0.60702
y' ≈ 2.32831

Therefore, the coordinates of the point (2, 2) after rotating it 136 degrees clockwise are approximately (-0.60702, 2.32831).