Question

12 cos θ - 16 sin θ = 0, find 2 sin θ + cos θ.

Answer 1

Given:

12 cos ⁡θ − 16 sin⁡ θ = 0 

Rearrange:

12 cos θ = 16 sin θ

Divide by cos ⁡θ:

12 = 16 tan θ 

tan θ = `12/16 = 3/4`

Find sin⁡ θ and cos⁡ θ from tan⁡ θ = `3/4`:

Hypotenuse = `sqrt(3^2 + 4^2 = 5)`

`sin θ = 3/5, cos θ = 4/5`

Required:

= 2 sin θ + cos θ

= 2 `(3/5) + 4/5`

= `6/5 + 4/5`

= `10/5 = 2`