Question

If $\sin \theta =\frac{5}{13}$ and $0<\theta <{90}^o$, find out the value of $\cos \theta$.

• A. $\frac{5}{12}$
• B. $\frac{12}{13}$
• C. $\frac{13}{12}$
• D. $\frac{12}{5}$

Answer 1

Answer: (B)

$\frac{12}{13}$

Given, $\sin \theta =\frac{5}{13}$

Since $0<\theta <{90}^0$

$\therefore \cos \theta$ and $\tan \theta$ are positive.

Thus ${\cos }^2\theta =1-{\sin }^2\theta$

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

$\Rightarrow {\cos }^2\theta =1-\frac{25}{169}$

$\Rightarrow {\cos }^2\theta =\frac{169-25}{169}$

$\Rightarrow {\cos }^2\theta =\frac{144}{169}$

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