Question

If `cos θ = 7/25`, find the values of other t-ratios.

Answer 1

1. Identify given sides

In a right-angled triangle, is defined as the ratio of the base (adjacent side) to the hypotenuse:

`cos θ = "Base"/"Hypotenuse"`

= `7/25`

Let the base be 7k and the hypotenuse be 25k.

2. Calculate the perpendicular side

Using the Pythagorean theorem (a² + b² = c²), we find the perpendicular (opposite side):

(Perpendicular)² = (Hypotenuse)² – (Base)²

(Perpendicular)² = 25² – 7²

= 625 – 49

= 576

Perpendicular = `sqrt(576)`

= 24

3. Determine the remaining ratios

Using the side lengths (Base = 7, Perpendicular = 24, Hypotenuse = 25), we calculate the other t-ratios:

`sin θ: "Perpendicular"/"Hypotenuse"`

= `24/25`

`tan θ: "Perpendicular"/"Base"`

= `24/7`

`"cosec"  θ: 1/(sin θ)`

= `25/24`

`sec θ: 1/(cos θ)`

= `25/7`

`cot θ: 1/(tan θ)`

= `7/24`