Find the radian measures corresponding to the following degree measures:
(i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520°

Solution:

A radian is another unit for the measurement of angle.

2π radian is equal to 360°.

By using 1° = π/180 radian,

we can convert the degree measures into radian measures.

⇒ 1° = π / 180 radian

or 1 radian = 180°/π

(i) 25° 

As we know that,

⇒ 1° = π / 180 radian.

We can write

⇒ 25° = π / 180 radian × 25.

By solving this, we get

⇒ 25° = 5π / 36 radian.

(ii) – 47° 30′

We know that 1º = 60' 

⇒ 1/2° = 30'

Therefore,

- 47° 30' = - 47 (1/2)°

⇒ - 95 / 2°

To convert it into radian measure,

⇒ 1° = π / 180 radian.

We can write

⇒ - 47 1/2° = π / 180 radian × (-95/2).

By solving this, we get

⇒ - 47 1/2° = - 19π / 72 radian

(iii) 240°

As we know that,

⇒ 1° = π / 180 radian.

We can write

⇒ 240° = π / 180 radian × 240.

By solving this, we get

⇒ 240° = 4π / 3 radian.

(iv) 520°

As we know that,

⇒ 1° = π / 180 radian.

We can write

⇒ 520° = π / 180 radian × 520.

By solving this, we get

⇒ 520° = 26π / 9 radian.

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NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.1 Question 1

Find the radian measures corresponding to the following degree measures:(i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520°

Summary:

Therefore, the radian measures corresponding to the given degree measures are (i) 5π / 36 radian, (ii) - 19π / 72 radian, (iii) 4π / 3 radian, and (iv) 26π / 9 radian