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

Answer:

$\sec A =\frac{\sqrt{13}}{3}$

Step-by-step explanation:

Given

$\tan A = 2/3$

Required

$\sec\ A$

First, we have:

$\tan A = \frac{x}{y}$

Where

$x \to oppo site$

$y \to adja cent$

$z \to hypotenuse$

So:

$\tan A = \frac{x}{y} =\frac{2}{3}$

By comparison:

$x = 2; y =3$

Using Pythagoras, we have:

$z^2 = x^2 +y^2$

$z^2 = 2^2 +3^2$

$z^2 = 13$

$z = \sqrt{13$

$\sec A =\frac{z}{y}$

$\sec A =\frac{\sqrt{13}}{3}$