find the cosine for an angle that has a sine of 340√/20 and is in quadrant ii. use the pythagorean identity sin^2(θ)+cos^2(θ)=1 and the quadrant to solve.(1 point) responses −110 negative start fraction 1 over 10 end fraction −10√10 negative start fraction 1 over start root 10 end root end fraction 110 start fraction 1 over 10 end fraction 10√10
To find the cosine of an angle, you can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1. Since the angle is in quadrant II, where the cosine is negative, the cosine would be represented as −√(1 - sin^2(θ)).
Given that the sine of the angle is 340√/20, we can simplify it as follows:
sin(θ) = 340√/20 = 17√10/20 = 17√10/(10√2) = √10/√2 = √5/2
Now, substitute this value into the equation for cosine:
cos(θ) = −√(1 - sin^2(θ))
= −√(1 - (√5/2)^2)
= −√(1 - 5/4)
= −√(4/4 - 5/4)
= −√(-1/4)
= −√(-1)/√4
= −√(-1)/2
= −(i)/2
Therefore, the cosine for an angle in the second quadrant with a sine of 340√/20 is −(i)/2.