evaluate the 6 trigonometric ratios if possible of the angle θ. (1- sin=1/2 , cos=- √3/2)

Question

ASTC rule, Use the given values to evaluate the 6 trigonometric ratios if possible of the angle θ. (1- sin=1/2 , cos=- √3/2)

Answer 1

1-sinθ=½, sinθ=½, θ=π/6 and 5π/6 using the ASTC Rule. We can add 2πn to each of these to find other values, where n is any integer.

cosθ=-√3/2, θ=5π/6 and 7π/6. We can add 2π to each of these to find other values.

But to satisfy both equations θ=5π/6 ± 2πn.

tanθ=-√3/3 and cotθ=-√3;

sinθ=½, cscθ=2;

cosθ=-√3/2, secθ=-2/√3=-2√3/3.