Question

The terminal side of theta in standard position contains the point (-4,-2).

Find the exact value for sine theta:

Answer 1

sin(θ) = -0.894

Explanation:

If we have a point (x, y), the angle formed between the positive x-axis and the ray that connects the origin with the point is given by:

tan(θ) = y/x

cos(θ) = y/√(x^2 + y^2)

sin(θ) = x/√(x^2 + y^2)

Here we have the point (-4, -2)

so we have:

x = -4

y = -2

Replacing these values in the sine equation, we get:

sin(θ) = -4/√((-4)^2 + (-2)^2)

sin(θ) = -0.894