Steph is told that an angle has a sine of 1/4 and is in Quadrant II. Use the Pythagorean identity sin^2(θ)+cos^2(θ)=1 , the trigonometric identity tanθ=sinθ/cosθ , and the quadrant to find the tangent. (1 point)
Let's use the given information to find the cosine of the angle in Quadrant II.
Since the sine is positive in Quadrant II, we know that the cosine must be negative. Using the Pythagorean identity:
sin^2(θ) + cos^2(θ) = 1
(1/4)^2 + cos^2(θ) = 1
1/16 + cos^2(θ) = 1
cos^2(θ) = 1 - 1/16
cos^2(θ) = 15/16
Taking the square root of both sides, we get:
cosθ = ± √(15/16)
Since the angle is in Quadrant II and the cosine is negative in that quadrant, we get:
cosθ = - √(15/16)
Now, we can use the trigonometric identity to find the tangent:
tanθ = sinθ/cosθ
tanθ = (1/4) / (- √(15/16))
tanθ = -1/4√(15/15)
tanθ = -√15/60
Therefore, the tangent of the angle is -√15/60.