Question

If `tan θ = 4/3`, find without using tables, the value of sin θ + cos θ (both sin θ and cos θ are positive).

Answer 1

Given: `tan θ = 4/3` and sin θ, cos θ > 0.

Step-wise calculation:

1. Represent triangle with opposite = 4, adjacent = 3.

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

= `sqrt(9 + 16)`

= `sqrt(25)`

= 5

3. `sin θ = "Opposite"/"Hypotenuse"`

= `4/5`

`cos θ = "Adjacent"/"Hypotenuse"`

= `3/5`

4. `sin θ + cos θ = 4/5 + 3/5`

= `7/5`

`sin θ + cos θ = 7/5`   ...(≈ 1.4)