R =(cos0 -sin0)
(sin0 -cos0)
State the matrix R for 0=120 degrees
NB 0 represents theta
To find the matrix R for θ = 120 degrees, we need to substitute θ = 120 degrees into the given matrix. Recall that in trigonometry, the cosine and sine of 120 degrees can be expressed as:
cos(120°) = -0.5
sin(120°) = √3 / 2
Now we can substitute these values into the matrix:
R = (cosθ -sinθ)
(sinθ -cosθ)
R = (cos120° -sin120°)
(sin120° -cos120°)
Replacing the values:
R = (-0.5 - (√3 / 2))
(√3 / 2 - (-0.5))
Simplifying, we get the final matrix:
R = (-0.5 -√3/2)
(√3/2 0.5)
Therefore, the matrix R for θ = 120 degrees is:
R = (-0.5 -√3/2)
(√3/2 0.5)