Question

Using tables, find the approximate value of θ, when cosec θ = 3.4.

Answer 1

Given: cosec θ = 3.4 ⇒ sin θ = `1/3.4` = 0.294117647...

Step-wise calculation:

1. From tables or by noting values.

sin 17° = 0.292372 and sin 18° = 0.309017

2. Target – sin 17°

= 0.294117647 – 0.292372 

= 0.001745647

3. Difference sin 18° – sin 17° = 0.016645.

So, one minute (1') change

= `0.016645/60` 

= 0.00027742

4. Required minutes

= `0.001745647/0.00027742`

= 6.29'

= 6.3'

5. Hence, θ = 17° + 6.3'

= 17°6.3'

= 17°6.4'

θ = 17°6.4'   ...(Approximately)