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 complementar

Answer 1

To solve the question, we need to recall the relationship between sine and cosine for complementary angles.

The angles 23° and 67° are complementary angles because:
\[ 23° + 67° = 90°. \]

According to the sine and cosine complementary angle identity, we have:
\[ \sin(90° - \theta) = \cos(\theta). \]

This means:
\[ \sin(67°) = \cos(23°). \]

Given that \( \cos(23°) = \frac{2}{3} \), we find that:
\[ \sin(67°) = \frac{2}{3}. \]

So the answer is **two thirds, because the angles are complementary**.