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=-(5)/(13)`

Now,

From the given equation,

`\begin{gathered} \cos \theta=-(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=-(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.