Question

What is cos θ when sin θ=3/5 and θ is in Quadrant II?

F. -4/5

G. -2/5

H. 2/5

I. 4/5

Answer 1

F

Explanation:

In Quadrant II, the sine of an angle is positive, but the cosine of an angle is negative. Given that sin θ = 3/5 and θ is in Quadrant II, we can use the Pythagorean identity to find the cosine of θ.

Using the Pythagorean identity:

sin² θ + cos² θ = 1

Substituting the given value:

(3/5)² + cos² θ = 1

9/25 + cos² θ = 1

cos² θ = 1 - 9/25

cos² θ = 16/25

cos θ = ±√(16/25)

Since we're in Quadrant II where the cosine is negative, we take the negative square root:

cos θ = -√(16/25)

cos θ = -4/5

Therefore, the value of cos θ when sin θ = 3/5 and θ is in Quadrant II is F. -4/5.