Question

If sin θ = 3 over 7 and tan θ < 0, what is the value of cos θ? (1 point)

Answer 1

The value of cos θ is -√(40/49).

Step-by-step explanation:

To find the value of cos θ, we can use the identity cos² θ + sin² θ = 1. We are given that sin θ = 3/7. Let's substitute this value into the identity:

cos² θ + (3/7)² = 1

cos² θ + 9/49 = 1

cos² θ = 40/49

cos θ = ±√(40/49)

Since tan θ < 0, θ must be in the second or fourth quadrant. In these quadrants, cos θ is negative. Therefore, cos θ = -√(40/49).

Answer 2

Answer:

−45

Step-by-step explanation:

Since tan(θ)=34>0 and sin(θ)<0, θ is in quadrant 3 (since tan(θ)>0 iff θ is in quadrant 1 or 3 and sin(θ)<0 iff θ is in quadrant 3 or 4).

cos(θ) must then be negative.