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).