Question

Assertion A :$\sin 1<\sin 1^0$
Reason R : $\sin x$ is a decreasing function in $(0,\frac{\pi }{2})$ .

• A. A , R are true and R is the correct explanation of A.
• B. A, R are true and R is not the correct explanation of A.
• C. Both A & R are false.
• D. A is true, R is false.

Answer 1

The correct option is C Both A & R are false.

${180}^0=\pi radians$

$1radian=\frac{180}{{\pi }^0}$

$1radian={57.32}^0$ $(\pi =3.14)approx$.

Now

$sin\left(x_1\right)>sin\left(x_2\right)$ if $x_1>x_2$ for all $x_1,x_2ϵ(0,\frac{\pi }{2})$.

Hence
$sin{57.32}^0>sin{1}^0$
or
$sin1>sin{1}^0$

Hence both A and R are false.