Given tan A = 4/3, find the other trigonometric ratios of the angle A.

Question

Given tan A = \(\frac{4}{3}\), find the other trigonometric ratios of the angle A.

Answer 1

Let us first draw a right ΔABC.

Now, we know that tan A = \(\frac{BC}{AB} = \frac{3}{4}\)

Therefore, if BC = 4k, then AB = 3k, where k is a positive number.

Now, by using the pythagoras theorem, we have

AC² = AB² + BC²

= (4k)² + (3k)² = 25 k²

AC = 5k

So,

Now, we can write all the trigonometric ratios using their definitions.