Question

If $\sec \theta =\frac{25}{7}$, then $\sin \theta =$

• A. $\frac{7}{24}$
• B. $\frac{24}{7}$
• C. $\frac{24}{25}$
• D. None of these

Answer 1

The correct option is C $\frac{24}{25}$

Trigonometric identity
${\sin }^2\theta +{\cos }^2\theta =1\Rightarrow {\sin }^2\theta =1-{\cos }^2\theta$

$\sec \theta =\frac{25}{7}\Rightarrow \cos \theta =\frac{7}{25}$

$\therefore {\sin }^2\theta =1-{\left(\frac{7}{25}\right)}^2=1-\frac{49}{625}=\frac{576}{625}$

$\Rightarrow \sin \theta =\frac{24}{25}$.