Question

If the cos 23° = two thirds, then the sin 67° = _____.

two thirds, because the angles are complementary
one half, because the angles are complementary
three halves, because the angles are supplementary
1, because the angles are complementary

Answer 1

The angles 23° and 67° are complementary, meaning that the sum of their measures equals 90° (23° + 67° = 90°).

According to the co-function identities, the sine of an angle is equal to the cosine of its complement:

\[
\sin(67°) = \cos(23°)
\]

Given that \(\cos(23°) = \frac{2}{3}\), we can substitute that into the equation:

\[
\sin(67°) = \frac{2}{3}
\]

Therefore, the answer is:

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