Question

Cos = -5/13 and sin 0 > 0. Identify the quadrant of 0 and find sin 0

Answer 1

Let's solve the equation for theta

`\begin{gathered} \cos \theta=-(5)/(13) \\ \theta=\cos ^(-1)(-(5)/(13)) \\ \theta\approx112.6 \end{gathered}`

This means angle theta is placed on the second quadrant.

We use Pythagorean's Theorem to find the other leg to find the sine function.

`\begin{gathered} 13^2=5^2+x^2 \\ x=\sqrt[]{13^2-5^2} \\ x=\sqrt[]{169-25} \\ x=\sqrt[]{144} \\ x=12 \end{gathered}`

It's important to know that the sine function is equivalent to the ratio between the opposite leg and the hypothenuse, and it has to be positive because sine functions are positive when the angle is on the second quadrant.

`\sin \theta=(12)/(13)`

Hence, the answer is C.