Question

For an acute angle $\theta$ in a right angled triangle, $\frac{\sin \theta }{\cos \theta }=$

• A. $\cot \theta$
• B. $\cos \theta$
• C. $\sin \theta$
• D. $\tan \theta$

Answer 1

The correct option is D $\tan \theta$

$\sin \theta =\frac{opposite}{hypotenuse}$

$\cos \theta =\frac{adjacent}{hypotenuse}$

$\frac{\sin \theta }{\cos \theta }=\frac{\frac{opposite}{hypotenuse}}{\frac{adjacent}{hypotenuse}}$

$=\frac{opposite}{adjacent}\times \frac{hypotenuse}{hypotenuse}$

$=\frac{opposite}{adjacent}$

$=\tan \theta$

Hence, $\frac{\sin \theta }{\cos \theta }=\tan \theta$.