Problem 22 - Precalculus Essentials

Question

Find a cofunction with the same value as the given expression. $$\sin 19^{\circ}$$

Step-by-Step Solution

Answer

The cofunction with the same value as \( \sin 19^{\circ} \) is \( \cos 71^{\circ} \).

Step 1: Identify the Complement of the Given Angle

To find the cofunction of \( \sin 19^{\circ} \), you first need to identify the complement of the given angle. This can be done by subtracting the given angle from 90 degrees, as complementary angles add up to 90 degrees: \( 90^{\circ} - 19^{\circ} = 71^{\circ} \)

Step 2: Identify the Cofunction of the Given Expression

Next, identify the cofunction that corresponds to the sine function. In trigonometry, the cofunction of the sine function is the cosine function. Therefore, you need to find the value of cosine at the complementary angle which is \( \cos 71^{\circ} \).

Step 3: Identify the Cofunction With the Same Value

Finally, you determine that \( \cos 71^{\circ} \) is the cofunction that generates the same value as \( \sin 19^{\circ} \).