Use the special triangles on the unit circle to determine θ in degrees when sinθ=3√2 .
(1 point)
Responses
45°
45°
90°
90°
30°
30°
60°
The special triangle for sinθ=3√2 has a hypotenuse of 1 (since it's on the unit circle) and a side length opposite the angle of sinθ equal to 3√2.
Using Pythagoras' theorem, we can find the length of the remaining side of the triangle:
(3√2)^2 + x^2 = 1^2
18 + x^2 = 1
x^2 = 1 - 18
x^2 = -17
Since the square root of a negative number is not defined in real numbers, there is no triangle on the unit circle with sinθ=3√2. Therefore, there is no value of θ in degrees that satisfies this equation.