Question
What is the sine for an angle that has a cosine of −4/7 and is in Quadrant II? Use the Pythagorean identity sin2(θ)+cos2(θ)=1 and the quadrant to solve.(1 point) Responses −33√7 negative Start Fraction Start Root 33 End Root over 7 End Fraction 33√7 Start Fraction Start Root 33 End Root over 7 End Fraction −3349 negative Start Fraction 33 over 49 End Fraction 3349
Answers
GPT 3.5
To find the sine of an angle in Quadrant II with a cosine of -4/7, we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1.
Since the angle is in Quadrant II, the sine will be positive.
We know that cos(θ) = -4/7.
Let's calculate sin(θ):
sin^2(θ) + cos^2(θ) = 1
sin^2(θ) + (-4/7)^2 = 1
sin^2(θ) + 16/49 = 1
sin^2(θ) = 1 - 16/49
sin^2(θ) = 33/49
Taking the square root of both sides gives:
sin(θ) = ± √(33/49)
Since the angle is in Quadrant II, sin(θ) is positive. Therefore, the sine of the angle is:
sin(θ) = √(33/49) = √33/7
So, the answer is √33/7.
Since the angle is in Quadrant II, the sine will be positive.
We know that cos(θ) = -4/7.
Let's calculate sin(θ):
sin^2(θ) + cos^2(θ) = 1
sin^2(θ) + (-4/7)^2 = 1
sin^2(θ) + 16/49 = 1
sin^2(θ) = 1 - 16/49
sin^2(θ) = 33/49
Taking the square root of both sides gives:
sin(θ) = ± √(33/49)
Since the angle is in Quadrant II, sin(θ) is positive. Therefore, the sine of the angle is:
sin(θ) = √(33/49) = √33/7
So, the answer is √33/7.