Question

Convert into radians 45° 20'
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Answer 1

Answer:

40° 20′ is equal to (121/540)π radians.

Step-by-step explanation:

According to the information provided in the question it is given as

45° 20'

We need to convert into radian

We know that, 1 degree = 60 min or 1° = 60′

40° 20′

= 40° + 20′

= 40° + (20°/60°)

= 40° + (1/3)°

= (120° + 1°)/3°

= 121°/3

Also,

Radian measure = (π/180°) × Degree measure

= (π/180°) × (121°/3)

= (121/540)π

Therefore, 40° 20′ is equal to (121/540)π radians.

Answer 2

Given, Degree measure 45° 20'

Find convert the degree measure into radians

Solution :-

Converting the minutes into degree :-

$\ast \: \boxed{ \orange{\textbf{\textsf{1° = 60'}}}}$

on substituting the values,

$\rm⇒ \: \: 40\degree + ( \frac{20}{60})°$

$\rm⇒ \: \: 40° + ( \frac{1}{3} )°$

$\rm⇒ \: \: \frac{120° + 1°}{3}$

$\rm⇒ \: \: \frac{121°}{3}$

as we know that, to convert Degree into radians we use the formula below,

$\boxed{ \bf{\tiny \bf{Radian \: measure= \frac{\pi}{180 \degree} \times\bigg(Degree \: measure \bigg)}}}$

on substituting the values,

$\rm⇢ \: \: Radian \: \: measure = \frac{\pi}{180} \times \frac{121}{3}$

$\bf⇢ \: \: Radian \: \: measure = ( \frac{121\pi}{540} ) \: radians$