Georgina is told that and angle has a sine of √5/5 and is in quadrant II. use the Pythagorean identity sin^2(0) + cos^2(0) = 1, the trigonometric identity tan0 = sin0/cos0 and the quadrant to find the tangent.
To find the tangent of the angle, we need to determine the cosine of the angle and then use the trigonometric identity tan(θ) = sin(θ)/cos(θ).
Given that the sine of the angle is √5/5, we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to find the cosine of the angle.
sin^2(θ) + cos^2(θ) = 1
(√5/5)^2 + cos^2(θ) = 1
5/25 + cos^2(θ) = 1
cos^2(θ) = 1 - 5/25
cos^2(θ) = 20/25
cos^2(θ) = 4/5
cos(θ) = ±√(4/5)
Since the angle is in quadrant II, the cosine is negative.
cos(θ) = -√(4/5)
Now, using the trigonometric identity tan(θ) = sin(θ)/cos(θ), we can find the tangent.
tan(θ) = sin(θ)/cos(θ)
tan(θ) = (√5/5)/(-√(4/5))
tan(θ) = (√5/5) * (-√(5/4))
tan(θ) = -√((5/5) * (5/4))
tan(θ) = -√(25/20)
tan(θ) = -√(5/4)
tan(θ) = -√5/√4
tan(θ) = -√5/2
Therefore, the tangent of the angle is -√5/2.