Question

Consider the following statements
Statement I The degree measure corresponding to $(-2)$ radian is $-114^{\circ} 19 \min$.
Statement II The degree measure of a given radian measure $=\frac{180}{\pi} \times$ Radian measure.
Choose the correct option.

• A. Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I
• B. Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
• C. Statement I is true; Statement II is false
• D. Statement I is false; Statement II is true

Answer 1

Answer: (D)

Statement II is true.
$\therefore$ Degree measure of $(-2)$ radian
$ =\frac{180}{\pi} \times-2$
$ =\frac{180}{22} \times-2 \times 7 \left(\because \pi=\frac{22}{7}\right)$
$ =\left(-\frac{1260}{11}\right)^{\circ}=-\left(114 \frac{6}{11}\right)^{\circ} $
$=-114^{\circ}\left(\frac{6}{11} \times 60\right)^{\prime} $
$ =-114^{\circ} 32^{\prime}\left(\frac{8}{11} \times 60\right)^{\prime \prime} $
$ =-114^{\circ} 32^{\prime} 43.6^{\prime \prime}$
$ =-114^{\circ} 32^{\prime} 44^{\prime \prime} \text { (approx.) }$
So, Statement $I$ is false.
So, correct option is (d).