Which expression is equivalent to $\cos (70°)$ using cofunctions of complementary angles?

• A. $\sin (20°)$
• B. $\tan (20°)$
• C. $\sin (70°)$
• D. $\cos (20°)$

Answer: (A)

Verified step by step guidance

1. Recall the cofunction identity for cosine and sine: \(\cos(\theta) = \sin(90^\circ - \theta)\), where the angles are complementary (sum to 90 degrees).
2. Identify the given angle \(\theta\) in the problem, which is \(70^\circ\).
3. Calculate the complementary angle by subtracting \(70^\circ\) from \(90^\circ\): \(90^\circ - 70^\circ = 20^\circ\).
4. Apply the cofunction identity by replacing \(\cos(70^\circ)\) with \(\sin(20^\circ)\).
5. Conclude that the expression equivalent to \(\cos(70^\circ)\) using cofunctions of complementary angles is \(\sin(20^\circ)\).