Question

Given that `tan θ = 5/12` and angle is an acute angle, find sin θ and cos θ.

Answer 1

Given: `tan θ = 5/12` and θ is acute.

Step-wise calculation:

1. Let opposite = 5k and adjacent = 12k

So, `tan θ = "Opposite"/"Adjacent"` 

= `5/12`

2. Hypotenuse = `sqrt((5k^2) + (12k^2)` 

= `sqrt(25k^2 + 144k^2)`

= `sqrt(169k^2)`

= 13k

3. `sin θ = "Opposite"/"Hypotenuse"`

= `(5k)/(13k)`

= `5/13`

4. `cos θ = "Adjacent"/"Hypotenuse"`   ...(Both positive because θ is acute.)

= `(12k)/(13k)`

= `12/13` 

`sin θ = 5/13, cos θ = 12/13`.