#### Question

In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`cos A = 4/5`

#### Solution

We know that `cos theta = "adjacent side"/"hypotenuse"`

Let us consider a right-angled ΔABC

Let opposite side BC = x.

By applying Pythagoras theorem, we get

𝐴𝐶^{2} = 𝐴𝐵^{2} + 𝐵𝐶^{2}

25 = x + 16

x = 25 - 16 = 9

x = `sqrt9 = 3`

We know that `cosA = 4/5`

`sin A = "opposite side"/"hypotenuse" = 3/5`

`tan A = "opposite side"/"adjacent side" = 3/4`

`cosec A = 1/(sin A) = (1/3)/5 = 5/3`

`sec A = 1/(cos A) = (1/4)/5 = 5/4`

`cot A = 1/(tan A) =(1/3)/4 = 4/3`

Is there an error in this question or solution?

#### APPEARS IN

Solution In the Following, Trigonometric Ratios Are Given. Find the Values of the Other Trigonometric Ratios. `Cos a = 4/5` Concept: Trigonometric Ratios.