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.

When $\theta =0^{\circ },sin\theta =0,cos\theta =1$ and $tan\theta =0$.

When $\theta ={30}^{\circ },sin\theta =\frac{1}{2},cos\theta =\frac{\sqrt{3}}{2}$ and $tan\theta =\frac{1}{\sqrt{3}}$.

When $\theta ={45}^{\circ },sin\theta =\frac{1}{\sqrt{2}},cos\theta =\frac{1}{\sqrt{2}}$ and $tan\theta =1$

When $\theta ={60}^{\circ },sin\theta =\frac{\sqrt{3}}{2},cos\theta =\frac{1}{2}$ and $tan\theta =\sqrt{3}$.

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.