Question

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

negative 6

−6–√

negative Start Root 6 End Root

6–√

Start Root 6 End Root
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Answer 1

Interpret cos θ = −1/√7 (in Quadrant III).

Compute sin²θ = 1 − cos²θ = 1 − (1/7) = 6/7, so sin θ = −√(6/7) (negative in QIII).

Then tan θ = sin θ / cos θ = [−√(6/7)] / [−1/√7] = √6.

Answer: √6.