Question

Find the radian measure corresponding to the following degree measures:
(i) 300^° (ii) 35^° (iii) -56^° (iv)135^° (v) -300^°
(vi) 7^° 30′ (vii) 125^° 30’ (viii) -47^° 30′

Answer 1

As we know that 180° = π rad ⇒ 1° = π/ 180 rad

(i) 300°

(300 × π/180) rad

5π/3
∴ Radian measure of 300^° is 5π/3

(ii) 35°

(35 × π/180) rad

7π/36

∴ Radian measure of 35^° is 7π/36

(iii) -56°

(-56 × π/180) rad

-14π/45

∴ Radian measure of -56° is -14π/45

(iv) 135°

(135 × π/180) rad

3π/4

∴ Radian measure of 135° is 3π/4

(v) -300°

(-300 × π/180) rad

-5π/3

∴ Radian measure of -300° is -5π/3

(vi) 7° 30′

As we know that, 30′ = (1/2)°

7° 30′ = (7 1/2)°

= (15/2)^°

= (15/2 × π/180) rad

= π/24

∴ Radian measure of 7° 30′ is π/24

(vii) 125° 30′

As we know that, 30′ = (1/2)°

125° 30’ = (125 1/2)°

= (251/2)^°

= (251/2 × π/180) rad

= 251π/360

∴ Radian measure of 125° 30′ is 251π/360

(viii) -47° 30′

As we know that, 30′ = (1/2)°

-47° 30’ = – (47 1/2)°

= – (95/2)^°

= – (95/2 × π/180) rad

= – 19π/72

Thus, radian measure of -47° 30′ is – 19π/72