Find the cosine for an angle that has a sine of 340√20 and is in Quadrant II. Use the Pythagorean identity sin2(θ)+cos2(θ)=1 and the quadrant to solve.(1 point)
Responses
−10√10
negative Start Fraction 1 over Start Root 10 End Root End Fraction
110
Start Fraction 1 over 10 End Fraction
10√10
Start Fraction 1 over Start Root 10 End Root End Fraction
−110
The sine of an angle in Quadrant II is always positive. Since the sine of the angle is given as 340√20, which is positive, we can conclude that the sine of the angle is positive.
Using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can solve for cos(θ):
(340√20)^2 + cos^2(θ) = 1
115600(20) + cos^2(θ) = 1
2312000 + cos^2(θ) = 1
cos^2(θ) = 1 - 2312000
cos^2(θ) = -2311999
Since the cosine of an angle can't be negative, we know that there is no real solution for cos(θ). Therefore, none of the given options are correct.