Question

if the $\cos 23^{\circ}=\frac{2}{3}$, then the $\sin 67^{\circ}=$
$\frac{2}{3}$, because the angles are complementary
$\frac{1}{2}$, because the angles are complementary
$\frac{3}{2}$, because the angles are supplementary
1, because the angles are complementary

Explanation:

Step1: Recall the co - function identity

The co - function identity states that \(\sin\theta=\cos(90^{\circ}-\theta)\) and \(\cos\theta = \sin(90^{\circ}-\theta)\).

Step2: Check the relationship between \(23^{\circ}\) and \(67^{\circ}\)

Since \(23^{\circ}+67^{\circ}=90^{\circ}\), the angles \(23^{\circ}\) and \(67^{\circ}\) are complementary.
Using the co - function identity \(\sin67^{\circ}=\cos(90^{\circ} - 67^{\circ})=\cos23^{\circ}\)

Answer:

\(\frac{2}{3}\), because the angles are complementary