Question

If $\cos \theta =\frac{5}{13}$, where ${}^{\prime }{\theta }^{\prime }$ is an acute angle. Find the value of $\sin \theta$.

Answer 1

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

We have to find $sin\theta$

We know that, $sin\theta =\sqrt{1-co{s}^2\theta }$

$sin\theta =\sqrt{1-{\left(\frac{5}{13}\right)}^2}$

$=\sqrt{1-\frac{25}{169}}$

$=\sqrt{\frac{169-25}{169}}$

$=\sqrt{\frac{144}{169}}$

$=\frac{12}{13}$

$\therefore sin\theta =\frac{12}{13}$