Question

if change 30 degree 30 minute 30 second into radian

Answer 1

30 degree 30 minute 30 second = $\dfrac{3661\pi}{21600}$ radian

Let us know some formulae first:

1. 30 seconds = 1 minute
2. 60 minutes = 1 degree
3. 180 degrees = π radian

We must see, 1 degree = $\dfrac{\pi}{180}$ radian

Step-by-step explanation:

We convert 30 degrees, 30 minutes and 30 seconds into radians one by one.

Step 1: 30 degrees into radians

Here, 30 degrees

= $30\times\dfrac{\pi}{180}$ radian

= $\dfrac{\pi}{6}$ radian

Step 2: 30 minutes into radians

Here, 30 minutes

= $\dfrac{30}{60}$ degree

= $\dfrac{1}{2}$ degree

= $\dfrac{1}{2}\times\dfrac{\pi}{180}$ radian

= $\dfrac{\pi}{360}$ radian

Step 3: 30 seconds into radians

Here, 30 seconds

= $\dfrac{30}{60}$ minute

= $\dfrac{1}{2}$ minute

= $\dfrac{1}{2\times 60}$ degree

= $\dfrac{1}{120}$ degree

= $\dfrac{1\times\pi}{120\times 180}$ radian

= $\dfrac{\pi}{21600}$ radian

Step 4: Find the sum of the radian values

Now, 30 degree 30 minute 30 second

= $\dfrac{\pi}{6}+\dfrac{\pi}{360}+\dfrac{\pi}{21600}$ radian

= $\dfrac{3600\pi+60\pi+\pi}{21600}$ radian

= $\dfrac{3661\pi}{21600}$ radian