Question

The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them $\frac{D}{90}=\frac{G}{100}=\frac{2C}{\pi }$ but $1^{\circ }={\left(\frac{180}{\pi }\right)}^{\circ }\simeq {57}^{\circ },{17}^{\prime },44.8^{\prime \prime }$ and sum of interior angles of a $n$-sided regular polygon is $(2n-4)\frac{\pi }{2}$. On the basis of above information, answer the following questions :Which of the following are correct

• A. $\sin 1^{\circ }<\sin 1^c$
• B. $\cos 1^{\circ }>\cos 1^c$
• C. $\cos 1^{\circ }<\cos 1^c$
• D. $1^c={57}^{\circ }\Rightarrow \sin 1^c<\sin {57}^{\circ }\Rightarrow \cos 1^c>\cos {57}^{\circ }$

Answer 1

Answer: (A), (B)

The correct options are
A $\sin 1^{\circ }<\sin 1^c$
B $\cos 1^{\circ }>\cos 1^c$

As $1^c={57}^0$
Then $\sin 1^0<\sin 1^c$ (since sine is increasing function)
And $\cos 1^0>\cos 1^c$ (as cosine is decreasing function)