Question

Hi, can you help to solve this exercise please !!!

Answer 1

Given:-

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

To find:-

The value of cos theta.

We know the formula,

`\sin ^2\theta+\cos ^2\theta=1`

From this formula, we derive the value of cos theta. we get,

`\begin{gathered} \sin ^2\theta+\cos ^2\theta=1 \\ \cos \theta=\sqrt[]{1-\sin ^2\theta} \end{gathered}`

Now we substitute the value of sin theta. so we get,

`\begin{gathered} \cos \theta=\sqrt[]{1-(12^2)/(13^2)} \\ \cos \theta=\sqrt[]{1-(144)/(169)} \\ \cos \theta=\sqrt[]{(169-144)/(169)} \\ \cos \theta=\sqrt[]{(25)/(169)} \\ \cos \theta=(5)/(13) \end{gathered}`

So the value of cos theta is,

`(5)/(13)`