Question

Say true or false:
$\tan \theta$ increases faster than $\sin \theta$ as $\theta$ increases.

• A. True
• B. False

Answer 1

The correct option is A True

Let us understand taking various cases of first quadrant,

$\sin \left(0^0\right)=0$

$\sin \left({30}^0\right)=\frac{1}{2}=0.5$

$\sin {45}^0=\frac{1}{\sqrt{2}}=0.707$

$\sin {60}^0=\frac{\sqrt{3}}{2}=0.866$

$\sin {90}^0=1$

Similarly

$\tan 0^0=0$

$\tan {30}^0=\frac{1}{\sqrt{3}}=0.577$

$\tan {45}^0=1$

$\tan {60}^0=\sqrt{3}=1.732$

$\tan {90}^0=\infty$

Hence

$\tan \theta$ increases faster than $\sin \theta$ as $\theta$ increases from $0^0$ to ${90}^0$.