Hi I need help solving this problem **Trigonometric Problem:**Given that \(\tan(\theta) = \frac{3}{4}\) and \(\theta\) is in Quadrant III, what is \(\cos(\theta)\)?**Explanation:**In trigonometry, the tangent function tan(θ) is a ratio of the opposite side to the adjacent side in a right triangle. The problem indicates that θ is in Quadrant III, where both sine and cosine are negative.To find \(\cos(\theta)\), use the Pythagorean identity:\[ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \]Given \( \tan(\theta) = \frac{3}{4} \), we set up a right triangle where:- Opposite side \(= 3k\)- Adjacent side \(= 4k\) Using the Pythagorean theorem:\[ (3k)^2 + (4k)^2 = h^2 \]\[ 9k^2 + 16k^2 = h^2 \]\[ 25k^2 = h^2 \]\[ h = 5k \]In Quadrant III, \(\cos(\theta)\) is negative, so:\[ \cos(\theta) = \frac{-4k}{5k} = -\frac{4}{5} \]Thus, \(\cos(\theta) = -\frac{4}{5}\).

Name: Hi I need help solving this problem **Trigonometric Problem:**Given th
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Hi I need help solving this problem **Trigonometric Problem:**Given that \(\tan(\theta) = \frac{3}{4}\) and \(\theta\) is in Quadrant III, what is \(\cos(\theta)\)?**Explanation:**In trigonometry, the tangent function tan(θ) is a ratio of the opposit