Question

Given that cosθ=2√2
of a triangle on the unit circle, what is the sine ratio of the same triangle?(1 point)
Responses

sinθ=2√2
sine theta is equal to the fraction with numerator square root of 2 and denominator 2

sinθ=3√2
sine theta is equal to the fraction with numerator square root of 3 and denominator 2

sinθ=1
sine theta is equal to 1

sinθ=12

Answer 1

Most likely the given cos θ is √2/2 (the entry "2√2" looks like a typo). Using the Pythagorean identity:

sin θ = ±√(1 − cos^2 θ) = ±√(1 − (√2/2)^2) = ±√(1 − 1/2) = ±√(1/2) = ±√2/2.

For a triangle on the unit circle (acute angle) take the positive value, so sin θ = √2/2.