Question

If `tan θ = 8/15`, find the values of other t-ratios.

Answer 1

Given: `tan θ = 8/15` assume θ is acute so all primary ratios are positive.

Step-wise calculation:

1. Interpret `tan θ = "Opposite"/"Adjacent"`

= `8/15`

2. Compute hypotenuse:

`r = sqrt(8^2 + 15^2)`

= `sqrt(64 + 225)`

= `sqrt(289)`

= 17

3. Use definitions:

`sin θ = "Opposite"/"Hypotenuse"`

= `8/17`

`cos θ = "Adjacent"/"Hypotenuse"`

= `15/17`

`cot θ = 1/(tan θ)`

= `"Adjacent"/"Opposite"`

= `15/8`

`sec θ = 1/(cos θ)`

= `"Hypotenuse"/"Adjacent"`

= `17/15`

`"cosec"  θ = 1/(sin θ)`

= `"Hypotenuse"/"Opposite"`

= `17/8`