Question

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

Answer 1

Given: The cosine function below

$\cos \theta=\frac{12}{13}$

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=\frac{5}{13}$

Using trigonometry identities,

$\sin 2\theta=2sin\theta\cos \theta$

Substituting into the identities

$\sin 2\theta=2\times\frac{5}{13}\times\frac{12}{13}=\frac{120}{169}$

Hence,

$\sin 2\theta=\frac{120}{169}$