Which of the following expressions is equivalent to $\sin (22°)$?

• A. $\sin (158°)$
• B. $\sin (-22°)$
• C. $\sin (68°)$
• D. $\cos (22°)$

Answer: (A)

Verified step by step guidance

1. Recall the sine function's key properties and identities, especially the sine of supplementary angles: \(\sin(\theta) = \sin(180^\circ - \theta)\).
2. Apply this identity to \(\sin(22^\circ)\) by calculating \$180^\circ - 22^\circ$ to find an equivalent angle.
3. Recognize that \(\sin(-\theta) = -\sin(\theta)\), so \(\sin(-22^\circ)\) is not equal to \(\sin(22^\circ)\) but rather its negative, which is different from the original value.
4. Consider the complementary angle identity: \(\sin(\theta) = \cos(90^\circ - \theta)\), and check if \(\cos(22^\circ)\) or \(\sin(68^\circ)\) matches \(\sin(22^\circ)\).
5. Conclude which expression(s) are equivalent to \(\sin(22^\circ)\) based on these identities and the values of the angles involved.