Problem 24 - Precalculus Essentials

Question

Find a cofunction with the same value as the given expression. $$\csc 35^{\circ}$$

Step-by-Step Solution

Answer

The cofunction with the same value as \(\csc 35^{\circ}\) is \(\sec 55^{\circ}\).

Step 1 Identify the given function and angle

The given function is \(\csc\) and the angle is \(35^{\circ}\). So we need to find the cofunction of \(\csc 35^{\circ}\).

Step 2 Use the cofunction identities

According to the cofunction identities in trigonometry, the cofunction of \(\csc θ\) is \(\sec (90^{\circ} - θ)\). Hence, substitute \(θ = 35^{\circ}\) into the equation.

Step 3 Calculate the complementary angle

Substitute \(θ = 35^{\circ}\) in \(\sec (90^{\circ} - θ)\), we get \(\sec (90^{\circ} - 35^{\circ})\). Calculate the value inside the brackets, that is, \(90^{\circ} - 35^{\circ} = 55^{\circ}\). So, our cofunction is \(\sec 55^{\circ}\).