Question

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

Answer 1

As per given by the question,

There are given that,

$\cos \theta=-\frac{5}{13}$

Now,

From the given equation,

$\begin{gathered} \cos \theta=-\frac{5}{13}=\frac{Base}{\text{Hypotenuse}} \\ \end{gathered}$

Then,

For finding the sine trigonometric function,

$\sin \theta=\frac{Perpendicula}{\text{Hypotenuse}}$

According to the question, there are hypotenuse is given.

Then, need to find the perpendicula with the help of pythagoras theorem.

So,

From the pythagoras theorem,

$(\text{Hypotenuse)}^2=(Base)^2+(perpendicula)^2$

Then,

$\begin{gathered} (\text{Hypotenuse)}^2=(Base)^2+(perpendicula)^2 \\ (13)^2=(-5)^2+(perpendicula)^2 \\ 169=25+(perpendicular)^2 \\ (perpendicular)^2=169-25 \\ (perpendicular)^2=144 \\ perpendicular=\sqrt[]{144} \\ perpendicular=12 \end{gathered}$

Then,

$\begin{gathered} \sin \theta=\frac{perpendicular}{\text{hypotenuse}} \\ \sin \theta=-\frac{12}{13} \end{gathered}$

Now,

According to the concept of quadrant, sine and cose function both are negative in third quadrant.

Hence, the option A is correct.