Answer:
Explanation:
To solve the equation 4(sin(θ)^2) = -6.25, we need to find the value of θ in degrees.
First, let's isolate the sine term by dividing both sides of the equation by 4:
sin(θ)^2 = -6.25/4
sin(θ)^2 = -1.5625
Next, we take the square root of both sides to eliminate the square:
sin(θ) = ±√(-1.5625)
Since we are looking for the smallest positive degree value, we only consider the positive square root:
sin(θ) = √(-1.5625)
Now, we need to find the angle whose sine equals √(-1.5625). However, the sine function is only defined for values between -1 and 1. Therefore, there is no real angle whose sine equals √(-1.5625).
As a result, there is no solution to the equation 4(sin(θ)^2) = -6.25, and none of the given answer choices (59.4°, 37.0⁰, 25.9°, 70.7°) are correct.