Question

If \(\sin \theta = \frac{3}{5}\) and $ \theta $ is in the first quadrant, what is $ \tan \theta $?

• A. $ \frac{3}{4} $
• B. $ \frac{4}{3} $
• C. $ \frac{5}{3} $
• D. $ \frac{3}{5} $

Hint:

Use the Pythagorean identity to find missing trigonometric values when one is given.

Answer 1

The Correct Option is A

Given: $ \sin \theta = \frac{3}{5} $, $ \theta $ in 1st quadrant
Use identity: $$ \sin^2 \theta + \cos^2 \theta = 1 $$
Substituting: $$ \left( \frac{3}{5} \right)^2 + \cos^2 \theta = 1 \Rightarrow \cos^2 \theta = 1 - \frac{9}{25} = \frac{16}{25} $$
Since $ \theta $ is in 1st quadrant, $ \cos \theta > 0 $: $$ \cos \theta = \sqrt{\frac{16}{25}} = \frac{4}{5} $$
Find $ \tan \theta = \frac{\sin \theta}{\cos \theta} $: $$ \tan \theta = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4} $$