Question

The point (-3, 1) is onlthe terminal side of angle O, in standard position. What are

the values of sine, cosine, and tangent of O? Make sure to show all work.

Answer 1

cos(θ) = -3/√10

sin(θ) = 1/√10

tan(θ) = -1/3

Explanation:

When we have a point (x, y), the angle generated between the positive x-axis and a ray that connects the origin and the point, is defined by:

cos(θ) = x/(√(x^2 + y^2))

sin(θ) = y/(√(x^2 + y^2))

tan(θ) = y/x

Now we have the point (-3, 1), then we have:

x = -3

y = 1

√(x^2 + y^2) = √((-3)^2 + 1^2) = √10

Then we just need to replace these values in the given formulas:

cos(θ) = x/(√(x^2 + y^2)) = -3/√10

sin(θ) = y/(√(x^2 + y^2)) = 1/√10

tan(θ) = y/x = 1/-3 = -1/3