Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Find the radian measures corresponding to the following degree measures.
(i) 25
(ii)
(iii) 
Text Solution
Verified by ExpertsThe correct answer is:
B
Conversion of Degrees to Radians:
To convert a degree measure to radians, we use the formula:
$$ ext{radians} = ext{degrees} imes \frac{\pi}{180} $$
Now, let’s convert each degree measure:
(i) 25 degrees:
$$ ext{radians} = 25 \times \frac{\pi}{180} = \frac{25\pi}{180} = \frac{5\pi}{36} $$
(ii) -47°30′:
Convert minutes to degrees:
-47°30′ = -47.5°
$$ ext{radians} = -47.5 \times \frac{\pi}{180} = -\frac{47.5\pi}{180} = -\frac{19\pi}{72} $$
(iii) 39°22′30″:
Convert minutes and seconds to degrees:
39°22′30″ = 39 + \frac{22}{60} + \frac{30}{3600} = 39.375°
$$ ext{radians} = 39.375 \times \frac{\pi}{180} = \frac{39.375\pi}{180} \approx \frac{63\pi}{288} $$
So, the correct answers for the conversions are as follows:
(i) $$ \frac{5\pi}{36} $$
(ii) $$ -\frac{19\pi}{72} $$
(iii) $$ \frac{63\pi}{288} $$
Therefore, option B corresponds to these conversions.
To convert a degree measure to radians, we use the formula:
$$ ext{radians} = ext{degrees} imes \frac{\pi}{180} $$
Now, let’s convert each degree measure:
(i) 25 degrees:
$$ ext{radians} = 25 \times \frac{\pi}{180} = \frac{25\pi}{180} = \frac{5\pi}{36} $$
(ii) -47°30′:
Convert minutes to degrees:
-47°30′ = -47.5°
$$ ext{radians} = -47.5 \times \frac{\pi}{180} = -\frac{47.5\pi}{180} = -\frac{19\pi}{72} $$
(iii) 39°22′30″:
Convert minutes and seconds to degrees:
39°22′30″ = 39 + \frac{22}{60} + \frac{30}{3600} = 39.375°
$$ ext{radians} = 39.375 \times \frac{\pi}{180} = \frac{39.375\pi}{180} \approx \frac{63\pi}{288} $$
So, the correct answers for the conversions are as follows:
(i) $$ \frac{5\pi}{36} $$
(ii) $$ -\frac{19\pi}{72} $$
(iii) $$ \frac{63\pi}{288} $$
Therefore, option B corresponds to these conversions.
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