Question

Georgina is told that an angle has a sine of 5√5
and is in Quadrant II. Use the Pythagorean identity sin2(θ)+cos2(θ)=1
, the trigonometric identity tanθ=sin​θ​cos​θ​
, and the quadrant to find the tangent.(1 point)
Responses

−12
negative 1 half

12
1 half

−5√5
negative the fraction with numerator square root of 5 and denominator 5

25√

Answer 1

First simplify the given sine: sin θ = 5√5/25 = √5/5.

Compute cos using sin^2+cos^2=1:
sin^2 θ = (√5/5)^2 = 1/5, so cos^2 θ = 1 − 1/5 = 4/5.
Since θ is in Quadrant II, cos θ < 0, so cos θ = −√(4/5) = −2/√5 = −2√5/5.

Now tan θ = sin θ / cos θ = (√5/5) / (−2√5/5) = −1/2.

Answer: −1/2.