Question

Using tables, find the value of 4 sin θ – 3 cos θ, when tan θ = 0.3726.

Answer 1

Given: tan θ = 0.3726.

Step-wise calculation:

1. From trigonometric tables. 

tan θ = 0.3726 corresponds to θ = 20°26′

2. From the same tables.

sin 20°26′ = 0.3491

And cos 20°26′ = 0.9371

3. Compute 4 sin θ – 3 cos θ:

4 sin θ = 4 × 0.3491

= 1.3964

3 cos θ = 3 × 0.9371

= 2.8113

4 sin θ – 3 cos θ = 1.3964 – 2.8113

= –1.4149

4 sin θ – 3 cos θ ≈ –1.4149   ...(≈ –1.415)