Question

if sin θ = 12/13 and cos θ < 0, what is tan θ?

Answer 1

\[\rm sin = \frac{ opposite }{ hypotenuse }~~~~ \cos = \frac{ adjacent }{ hypotenuse } ~~\tan= \frac{ opposite }{ adjacent }\]

Answer 2

make a right triangle
sin is opposite over hypotenuse
12/13=opposite /hypotenuse
and then use Pythagorean theorem to find 3rd side of right triangle \[\huge\rm a^2 +b^2 =c^2\]

Answer 3

We can set up a triangle and find the missing side.

Recall SOH-CAH-TOA.
SOH = sin = opposite/hypotenuse

We can use the pythagorean theorem to find the value of the other side.



\[a^2 + b^2 = c^2\]
\[12^3 + 13^2 = c^2\]
\[\sqrt{c^2}\]