Find cos θ if sin θ = negative twelve divided by thirteen and tan θ > 0. negative five divided by twelve negative five divided by thirteen twelve divided by five negative thirteen divided by twelve

1.
Sin∅=opposite side / hypotenuse, in a right triangle, as shown in the figure.

In this triangle, the length of the hypotenuse is 13, the length of one side 12, and the other side can be found by the Pythagorean theorem to be:



2.
The value of the cosine is (adjacent side)/(hypotenuse)=5/13.

3.
The tangent is positive in the first and third quadrants.

Since Tan=Sine/Cosine, and Sine is negative, then cosine must be negative as well

-5/13

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