Question

If tan A = \(\frac{4}{3}\), find sin A and cos A.

Hint:

Memorize Pythagorean triplets like (3, 4, 5), (5, 12, 13) to solve these problems instantly.

Answer 1

Step 1: Given Value
tan A = 4/3

This means:
Opposite / Adjacent = 4/3

Let Opposite = 4k
Let Adjacent = 3k

Step 2: Find Hypotenuse
Using Pythagoras theorem:
H² = (4k)² + (3k)²
= 16k² + 9k²
= 25k²

H = 5k

Step 3: Find sin A and cos A
sin A = Opposite / Hypotenuse
= 4k / 5k
= 4/5

cos A = Adjacent / Hypotenuse
= 3k / 5k
= 3/5

Final Answer:
sin A = 4/5
cos A = 3/5