Question

If \(\tan\theta = -4/3\), then the value of \(\sin\theta\) is

• A. \(-4/5\) and not \(4/5\)
• B. \(-4/5\) or \(4/5\)
• C. \(4/5\) and not \(-4/5\)
• D. \(1/5\)

Hint:

Quadrant determines sign of trigonometric functions.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
\(\tan\) negative \(\rightarrow \theta\) in II or IV quadrant.
Step 2: Detailed Explanation:
\(\tan\theta = -4/3 \rightarrow \sin\theta = \pm 4/5\)
In II quadrant: \(\sin\) positive = \(4/5\)
In IV quadrant: \(\sin\) negative = \(-4/5\)
Step 3: Final Answer:
\(\sin\theta = \pm 4/5\).