Question

Which of the following statements is/are true for $\theta$ ranging from $0^{\circ }$ to ${90}^{\circ }$?

• A. $cos\theta ,cot\theta andcosec\theta$ increases as $\theta$ increases.
• B. $sin\theta ,tan\theta andsec\theta$ increases as $\theta$ increases.
• C. Trigonometric ratios values do not follow any pattern.
• D. $sin\theta =cos\theta$ for all the values of $\theta$

Answer 1

The correct option is B $sin\theta ,tan\theta andsec\theta$ increases as $\theta$ increases.

Trigonometric angles for some specific angles are given below:

$\begin{array}{cccccc}\theta & 0^{\circ }& {30}^{\circ }& {45}^{\circ }& {60}^{\circ }& {90}^{\circ }\\ sin\theta & 0& \frac{1}{2}& \frac{1}{\sqrt{2}}& \frac{\sqrt{3}}{2}& 1\\ cos\theta & 1& \frac{\sqrt{3}}{2}& \frac{1}{\sqrt{2}}& \frac{1}{2}& 0\\ tan\theta & 0& \frac{1}{\sqrt{3}}& 1& \sqrt{3}& Notdefined\end{array}$

Observe that as the value of $\theta$ increases, the values of $sin\theta$ and $tan\theta$ increase and the value of $cos\theta$ decreases.
We know that $sec\theta =\frac{1}{cos\theta }$.Thus, the value of $sec\theta$ increases, as the value of $cos\theta$ decreases.