Question

Given Tan A= 2/3 and that angle A is in quadrant 1, find the exact value of sec A in simplest radical form using a rational denominator.

Answer 1

`\sec A =(√(13))/(3)`

Explanation:

Given

`\tan A = 2/3`

Required

`\sec\ A`

First, we have:

`\tan A = (x)/(y)`

Where

`x \to oppo site\\`

`y \to adja cent`

`z \to hypotenuse`

So:

`\tan A = (x)/(y) =(2)/(3)`

By comparison:

`x = 2; y =3`

Using Pythagoras, we have:

`z^2 = x^2 +y^2`

`z^2 = 2^2 +3^2`

`z^2 = 13`

`z = \sqrt{13`

`\sec A =(z)/(y)`

`\sec A =(√(13))/(3)`