Using the Pythagorean Identity, determine cosθ if sinθ=79 and π2<θ<π .(1 point)
Responses
42√9
Start Fraction 4 Start Root 2 End Root over 9 End Fraction
−42√9
negative Start Fraction 4 Start Root 2 End Root over 9 End Fraction
−2√3
negative Start Fraction Start Root 2 End Root over 3 End Fraction
2√3
Using the Pythagorean Identity, we have:
cos^2θ + sin^2θ = 1
Substituting sinθ = 79, we have:
cos^2θ + 79^2 = 1
cos^2θ + 6241 = 1
cos^2θ = 1 - 6241
cos^2θ = -6240
Taking the square root of both sides and considering that π/2 < θ < π (which means cosθ < 0), we have:
cosθ = -√6240
After simplification, cosθ = -2√3.
Therefore, the correct response is: -2√3.