Question

Find the radian measure corresponding to the following degree measure : 5degree 37’30”

Answer 1

Dear student,.....We know that , 1' = 60'' ∴ 1'' = 1/60'..... ∴ 30'' = 30 / 60'..... = 0.5'..... ∴ 5°37' 30'' = 5° 37' 0.5' = 5°37.5' Then, 1' = 1/60°..... ∴ 37.5' = 37.5/60°..... =0.625°..... Thus, 5°37'30'' = 5°+0.625°..... ⇒5.625° ... Now, 360°= 2Ï€ rad... 1° =Ï€/180 rad....... ∴ 5.625° = 5.625Ï€ /180 rad...... = [ 5.625 ×(22/7) ] / 180 rad...... = 17.68 /180 rad...... = 0.09821 rad.... =9.821 × 10⁻² radian......Regards.