If sin theta = - 5/7, which of the following are possible?

a. cos theta = - √24/7, and tan theta=5/√24

b sec theta = 7/√24, and tan theta = - 5/√24

c. sec theta = - 7/5, and tan theta = 5/√24

d cos theta = √24/7, and tan theta = 5/√24

A) cos θ = - (√24) / 7 and tan θ = 5/√24 and

B) sec θ = 7 / (√24) and tan θ = - 5 / (√24)

Sine is the ratio of the opposite side of an angle to the hypotenuse. Since sin θ = - 5/7, the opposite side is - 5 and the hypotenuse is 7.

For A, if the cosine is - √24/7, and the sine was - 5/7, then the opposite/adjacent, tangent, would be - 5 / - (√24). However, two negatives divided make a positive, so the tangent would be 5/√24.

For B: the secant is 1/cos. This means it is the reciprocal, or flip, of the cosine. Instead of A/H, sec = H/A. This means the hypotenuse is 7 and the adjacent side is √24. Tangent = opposite/adjacent; this gives us - 5/√24.

For C: the secant, H/A, is - 7/5. This means the tangent, O/A, would be - 5/5 = - 1. This is incorrect.

For D: the cosine, A/H, is √24/7. This means the tangent, O/A, would be - 5/√24; this is incorrect.