Question

How do we write `6` radians, `3/4` radians and `-3` radians in degrees?

Answer 1

(i) `6` radians are `343.776^@` or `343^@46'33.6''`;
(ii) `3/4` radians are `42.972^@` or `42^@58'19.2''` and
(iii) `-3` radians are `-171.888^@` or `171^@53'16.8''`

Explanation:

As `pi` radians are `180^@`. one radian is `180^@/pi=57.296^@`.

Now `0.296^@=0.296xx60'=17.76'` and `0.76'=0.76xx60''= 45.6''`

Hence one radian is `57^@17'45.6''`

Hence,

(i) `6` radians are `6xx57.296^@=343.776^@` or `6xx57^@17'45.6''=343^@46'33.6''`

(ii) `3/4` radians are `3/4xx57.296^@=42.972^@=42^@58'19.2''`

(iii) `-3` radians are `-3xx57.296^@=-171.888^@=171^@53'16.8''`

While multiplying or dividing always remember that `1^@=60'` and `1'=60''`