Question

The value of \(\sin \theta\) or \(cosθ\) never exceeds

• A. -1
• B. 1
• C. 0
• D. none of these

Answer 1

The Correct Option is B

To solve the problem, we need to determine the maximum value that \( \sin \theta \) or \( \cos \theta \) can attain. Let us analyze this step by step.

1. Understanding the Range of \( \sin \theta \) and \( \cos \theta \):
The sine and cosine functions are trigonometric functions defined for all real numbers \( \theta \). Their values are bounded within a specific range:

$$ -1 \leq \sin \theta \leq 1 $$

$$ -1 \leq \cos \theta \leq 1 $$

This means both \( \sin \theta \) and \( \cos \theta \) can take any value between \(-1\) and \(1\), inclusive.

2. Maximum Value:
The maximum value that either \( \sin \theta \) or \( \cos \theta \) can attain is \( 1 \). This occurs when:

• For \( \sin \theta \), \( \theta = 90^\circ + 360^\circ k \) (or \( \frac{\pi}{2} + 2\pi k \) in radians), where \( k \) is an integer.
• For \( \cos \theta \), \( \theta = 0^\circ + 360^\circ k \) (or \( 0 + 2\pi k \) in radians), where \( k \) is an integer.

3. Conclusion:
Both \( \sin \theta \) and \( \cos \theta \) never exceed \( 1 \).

Final Answer:
The correct option is \( {1} \).