Question

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

Hint:

Draw a right triangle based on the ratio to avoid mistakes in identifying sides and computing the hypotenuse.

Answer 1

Step 1: Assume triangle sides using the given tangent ratio: \[ \tan A = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{3}{4} \] Step 2: Use Pythagoras theorem to find hypotenuse: \[ \text{Hypotenuse} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] Step 3: Use definitions of trigonometric ratios: \[ \sin A = \frac{3}{5}, \quad \sec A = \frac{5}{4} \] Final Answer: \[ \boxed{\sin A = \frac{3}{5}, \quad \sec A = \frac{5}{4}} \]