Question

Need help with pre caculas math pls it is hard for me

Answer 1

Given: The cosine function below

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

To Determine: the value of

`\sin 2\theta`

Given that the angle is acute, we can represent this using a right-angles triangle to determine the dimension of the third side

Using the Pythagoras theorem, we can get the value of the opposite sides

`\begin{gathered} a^2+12^2=13^2,a=\text{opposite} \\ a^2+144=169 \\ a^2=169-144 \\ a^2=25 \\ a=\sqrt[]{25}=5 \end{gathered}`
`\sin \theta=(5)/(13)`

Using trigonometry identities,

`\sin 2\theta=2sin\theta\cos \theta`

Substituting into the identities

`\sin 2\theta=2*(5)/(13)*(12)/(13)=(120)/(169)`

Hence,

`\sin 2\theta=(120)/(169)`