Question

What is the tangent for an angle that has a cosine of −17√
and is in Quadrant III? Use the Pythagorean identity sin2θ+cos2θ=1
, the trigonometric identity tanθ=sinθcosθ
, and the quadrant to solve. (1 point)
Responses

6
6

6–√

Start Root 6 End Root

−6

negative 6

−6–√

Answer 1

cos θ = -1/√7. Then sin^2 θ = 1 - cos^2 θ = 1 - 1/7 = 6/7, so sin θ = -√(6/7) (Quadrant III → sin negative).

tan θ = sin θ / cos θ = (-√(6/7))/(-1/√7) = √6.