Question

Which of the following is not correct?

• A. \( \sin 2\pi = \sin(-2\pi) \)
• B. \( \sin 4\pi = \sin 6\pi \)
• C. \( \tan 45^\circ = \tan(-315^\circ) \)
• D. \( \cos 5\pi = \cos 4\pi \)

Hint:

When evaluating trigonometric identities, always remember their periodic properties to determine the correctness of the statements.

Answer 1

The Correct Option is D

Let's evaluate each option: - Option 1: \[ \sin 2\pi = \sin(-2\pi) \quad \text{is true since} \quad \sin \theta \text{ is periodic with period } 2\pi. \] - Option 2: \[ \sin 4\pi = \sin 6\pi \quad \text{is true since} \quad \sin \theta \text{ is periodic with period } 2\pi. \] - Option 3: \[ \tan 45^\circ = \tan(-315^\circ) \quad \text{is true since} \quad \tan \theta \text{ is periodic with period } 180^\circ. \] - Option 4: \[ \cos 5\pi \neq \cos 4\pi \quad \text{because} \quad \cos \theta \text{ is periodic with period } 2\pi. \] Thus, \( \cos 5\pi = \cos \pi = -1 \) and \( \cos 4\pi = \cos 0 = 1 \), so the statement is false.