Question

Find the degree measures corresponding to the following radian measures . (i) (ii) – 4 (iii) (iv)

Answer 1

(i)

The degree measure is 25° .

π radian=180° 1°= π 180  radian

Multiply both sides by 25 .

25°=25× π 180  radian =0.436 radian

Thus, 25° is 0.436 radian .

(ii)

The degree measure is −47°3 0 ′ or −( 47°+3 0 ′ )

π radian=180° 1°= π 180  radian

Multiply both sides by 47 .

47°=47× π 180  radian =0.819 radian

Also,

1°=6 0 ′

So,

6 0 ′ = π 180  radian 1 ′ = π 60×180  radian

Multiply both sides by 30 .

3 0 ′ =30× π 60×180  radian =0.00873 radian

The total measure of −47°3 0 ′ is

( 0.819 +0.00873 )radian 0.82773 radian

Thus, −47°3 0 ′ is 0.82773 radian .

(iii)

The degree measure is 240° .

π radian=180° 1°= π 180  radian

Multiply both sides by 240 .

240°=240× π 180  radian =4.186 radian

Thus, 240° is 4.186 radian .

(iv)

The degree measure is 520° x−μ σ .

π radian=180° 1°= π 180  radian

Multiply both sides by 520 .

520°=520× π 180  radian =9.079 radian

Thus, 520° is 9.079 radian .