Question:
If \( \cos 76^\circ = \cos \left( 90^\circ - \theta \right) \), then the general value of \( \theta \) is
If \( \cos 76^\circ = \cos \left( 90^\circ - \theta \right) \), then the general value of \( \theta \) is
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When solving trigonometric equations, consider both possible solutions for angles due to periodicity and symmetry of trigonometric functions.
Updated On: Mar 25, 2026
- \( 76^\circ \)
- \( 90^\circ - 76^\circ \)
- \( 76^\circ \) and \( 180^\circ - 76^\circ \)
- \( 180^\circ - 76^\circ \)
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The Correct Option is C
Solution and Explanation
Step 1: Use the identity \( \cos \left( 90^\circ - \theta \right) = \sin \theta \).
This gives: \[ \cos 76^\circ = \sin \theta \] Therefore, \( \theta = 76^\circ \) or \( \theta = 180^\circ - 76^\circ = 104^\circ \).
Step 2: Conclusion.
The general value of \( \theta \) is \( 76^\circ \) and \( 180^\circ - 76^\circ \). Final Answer: \[ \boxed{76^\circ \text{ and } 180^\circ - 76^\circ} \]
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