Question

Consider this equation. cos ( θ ) = - 2 ⁢ 5 5 if θ is an angle in quadrant ii, what is the value of sin ( θ ) ? a. 5 5 b. - 1 2 c. - 5 5 d.

Answer 1

The value of sin(θ) is not defined for the given equation in quadrant II.

Step-by-step explanation:

To find the value of sin(θ) given the equation cos(θ) = -25/5 in quadrant II, we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1. Since cos(θ) = -25/5, we can substitute this value into the equation to solve for sin(θ).

cos^2(θ) + sin^2(θ) = 1
-25/5^2 + sin^2(θ) = 1
sin^2(θ) = 1 - (-25/5)^2
sin^2(θ) = 1 - 625/25
sin^2(θ) = 1 - 25
sin^2(θ) = -24

Since sin^2(θ) is negative, there is no real value for sin(θ) in quadrant II. Therefore, the value of sin(θ) is not defined for the given equation in this quadrant.