Question

which pair of angles has congruent values for the sin x° and the cos y°? 42°, 132° 42°, 138° 42°, 48° 42°, 42°

Explanation:

Step1: Recall the co - function identity

The co - function identity states that \(\sin x=\cos(90 - x)\). We need to check each pair.
For a pair \((x,y)\), we want to find when \(\sin x=\cos y\), i.e., \(y = 90 - x\).

Step2: Check each option

• Option 1: \(x = 42^{\circ},y = 132^{\circ}\)

\(\sin42^{\circ}
eq\cos132^{\circ}\) since \(\cos132^{\circ}=\cos(90 + 42)^{\circ}=-\sin42^{\circ}\)

• Option 2: \(x = 42^{\circ},y = 138^{\circ}\)

\(\sin42^{\circ}
eq\cos138^{\circ}\) since \(\cos138^{\circ}=\cos(90+48)^{\circ}=-\sin48^{\circ}\)

• Option 3: \(x = 42^{\circ},y = 48^{\circ}\)

Using the co - function identity \(\sin x=\cos(90 - x)\), when \(x = 42^{\circ}\), then \(\sin42^{\circ}=\cos(90 - 42)^{\circ}=\cos48^{\circ}\)

• Option 4: \(x = 42^{\circ},y = 42^{\circ}\)

\(\sin42^{\circ}
eq\cos42^{\circ}\) (since \(\sin42^{\circ}\approx0.6691\) and \(\cos42^{\circ}\approx0.7431\))

Answer:

\(42^{\circ},48^{\circ}\)