Trigonometric function....

Question

Answer 1

x is 4, the hypotenuse (r, radius in circle) is √41, So y= √((√41)²-4²)=5

tan(angle)=y/x=5/4

Answer 2

tanθ = sinθ/cosθ; sinθ = ±√(1 - 16/41) = ±5/(±√41); tanθ = ±5/4.

We can't make chose for sign: if θ in quadrant I, then tanθ = 5/4; if θ in quadrant IV then tanθ = -5/4

Answer 3

θ = arccos(4/√41) ≅ 51.34°

tan(51.34°) ≅ 1.24999

Answer 4

sin(theta)^2 + cos(theta)^2 = 1

so sin(theta)^2 + 16/41 = 1

sin(theta)^2 = 25/41

sin(theta) = 5/sqrt(41)

tan(theta) = sin(theta)/cos(theta) = 5/4