Question

cos degree= 4/5 and sin is less than 0 Identify the quadrant of the terminal side of degree and find sin degree

Answer 1

The quadrant is either the third or fourth quadrant and sin θ = -3/5.

Step-by-step explanation:

Given that cos θ = 4/5 and sin θ is less than 0, we can determine the quadrant of the terminal side of θ using the signs of the sine and cosine functions in each quadrant. Since sin θ is negative, it means that θ lies in either the third or fourth quadrant.

To find sin θ, we can use the Pythagorean identity: sin^2 θ + cos^2 θ = 1.

Substituting cos θ = 4/5 into the equation, we can solve for sin θ:

sin^2 θ + (4/5)^2 = 1

sin^2 θ + 16/25 = 1

sin^2 θ = 1 - 16/25

sin^2 θ = 9/25

sin θ = ± 3/5

Since sin θ is negative, we can conclude that sin θ = -3/5.