help with vector queston

Question

As part of video game, the point (3,2) is rotated counterclockwise about the origin through an angle of 5 degrees.

Find the new coordinates of this point

Answer 1

Initial angle:

θ₁ = arctan(2/3) = 33.7°

r = √(3² + 2²) = √13

Final angle:

θ₂ = θ₁ + 5° = (33.7 + 5) = 38.7°

x₂ = r cosθ₂ = √13 cos38.7° = ?

y₂ = r sinθ₂ = √13 sin38.7° = ?

Answer 2

tan θ = 0.667

tan (θ + 5) = (tan θ + tan 5) / (1 - tan θ tan 5)

tan (θ + 5) = (0.667 + 0,087) / (1 - (0.667)(0,087)

tan (θ + 5) ≈ 0.75 / 0.25

(0.25, 0.75)