Problem 21 - Precalculus Essentials

Question

Find a cofunction with the same value as the given expression. $$\sin 7^{\circ}$$

Step-by-Step Solution

Answer

The cofunction with the same value as \(\sin 7^{\circ}\) is \(\cos 83^{\circ}\).

Step 1: Identify the cofunction of sine

The cofunction of sine is cosine. Therefore, what needs to be found is a value for which the cosine gives the same result as \(\sin 7^{\circ}\).

Step 2: Find out for which angle cosine will give the same value

Since sine and cosine are complementary, the cosine of the complementary angle to 7 degrees, which is \(90 - 7 = 83\) degrees, will give the same value as \(\sin 7^{\circ}\).

Step 3: Write down the final cofunction

Having determined the needed angle, the cofunction with the same value as the given expression \(\sin 7^{\circ}\) is \(\cos 83^{\circ}\).