Which expression is equivalent to $\sin (22\circ )$ using cofunctions of complementary angles?

• A. $\cos (68\circ )$
• B. $\cos (22\circ )$
• C. $\tan (68\circ )$
• D. $\sin (68\circ )$

Answer: (A)

Verified step by step guidance

1. Recall the cofunction identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\).
2. Identify the given angle in the problem, which is \(22^\circ\).
3. Apply the cofunction identity by substituting \(\theta = 22^\circ\) into the formula: \(\sin(22^\circ) = \cos(90^\circ - 22^\circ)\).
4. Simplify the expression inside the cosine function: \(90^\circ - 22^\circ = 68^\circ\).
5. Conclude that \(\sin(22^\circ)\) is equivalent to \(\cos(68^\circ)\) using the cofunction identity.