Q(2) Find the degree measures corresponding to the following radian measures.  (Use \small \pi =\frac{22}{7})

 \small (i) \frac{11}{16}
\small (ii) -4
\small (iii) \frac{5\pi }{3}
\small (iv) \frac{7\pi }{6}

Answers (1)

Solution 

(1)   \frac{11}{16}

We know that 
    \pi radian   = 180\degree \Rightarrow 1 radian = \frac{180}{\pi} degree

So,   \frac{11}{16} radian = \frac{180}{\pi}\times \frac{11}{16}degree                            (we need to take \pi = \frac{22}{7} )

   \frac{11}{16}radian = \frac{180\times 7}{22}\times \frac{11}{16}degree \Rightarrow \frac{315}{8}degree 
 
                                                                                             (we use 1\degree = 60' and 1' = 60'')

Here 1' represents 1 minute and 60" represents 60 seconds
Now, 

\frac{315}{8}degree=39\frac{3}{8}degree\\ \\ =39\degree +\frac{3\times 60}{8}minutes \Rightarrow 39\degree +22' + \frac{1}{2}minutes \Rightarrow 39\degree +22' +30''\\ \\ \Rightarrow \frac{315}{8}degree = 39\degree22'30''                                                                                                             

(ii)  -4
We know that

\pi radian   = 180\degree \Rightarrow 1 radian = \frac{180}{\pi} degree             (we need to take \pi = \frac{22}{7} )


So,  -4 radian =  \frac{-4\times 180}{\pi} \Rightarrow \frac{-4\times 180\times 7}{22} \Rightarrow \frac{-2520}{11}degree                                                                                                                   


                                                                                            (we use 1\degree = 60' and 1' = 60'')

\Rightarrow \frac{-2520}{11}degree = -229\frac{1}{11}degree =-229\degree + \frac{1\times 60}{11}minutes \\ \\ \Rightarrow -229\degree + 5' + \frac{5}{11}minutes = -229\degree +5' +27''\\ \\ -\frac{2520}{11} = -229\degree5'27''


(iii)   \frac{5\pi}{3}

We know that 
    \pi radian   = 180\degree \Rightarrow 1 radian = \frac{180}{\pi} degree    (we need to take \pi = \frac{22}{7} )


So,  \frac{5\pi}{3}radian = \frac{180}{\pi}\times \frac{5\pi}{3}degree = 300\degree       
(iv)  \frac{7\pi}{6}

We know that 
    \pi radian   = 180\degree \Rightarrow 1 radian = \frac{180}{\pi} degree        (we need to take \pi = \frac{22}{7} )


So, \frac{7\pi}{6}radian = \frac{180}{\pi}\times \frac{7\pi}{6} = 210\degree           

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions