Question

Evaluate the six trigonometric functions of the angle θ x = 4, y = -5

Answer 1

To evaluate the six trigonometric functions of the angle θ with x = 4 and y = -5, use the formulas for sine, cosine, tangent, cosecant, secant, and cotangent.

Step-by-step explanation:

To evaluate the six trigonometric functions of the angle θ, we need to determine the values of the adjacent side (x) and the opposite side (y). In this case, x = 4 and y = -5.

The six trigonometric functions are:

1. Sine (θ) = y/h = -5/√(4^2 + (-5)^2) = -5/√41
2. Cosine (θ) = x/h = 4/√41
3. Tangent (θ) = y/x = -5/4
4. Cosecant (θ) = 1/sin(θ) = √41/(-5)
5. Secant (θ) = 1/cos(θ) = √41/4
6. Cotangent (θ) = 1/tan(θ) = 4/(-5)