Question

Using tables, find the approximate value of θ, when sec θ = 5.6.

Answer 1

Given: sec θ = 5.6

Step-wise calculation:

1. `sec θ = 1/cos θ` 

⇒ `cos θ = 1/5.6`

= 0.1785714286

2. From trig tables:

cos 79° = 0.190809

cos 80° = 0.173648

So, θ is between 79° and 80°.

3. Interpolate between 79° and 80°:

Δcos (79° → 80°) = 0.190809 – 0.173648 

= 0.017161

Δ to target = 0.190809 – 0.178571

= 0.012238

Fraction = `0.012238/0.017161`

= 0.7132

Minutes = 0.7132 × 60

= 42.79′

θ ≈ 79° 42.8′   ...(≈ 79° 43′)