Question

use the image below to answer the following question. what relationship do the ratios of \\(\sin x^\circ\\) and \\(\cos y^\circ\\) share? (1 point)

• the ratios are opposites (\\(\frac{-6}{8}\\) and \\(\frac{6}{8}\\)).
• the ratios are reciprocals (\\(\frac{6}{8}\\) and \\(\frac{8}{6}\\)).
• the ratios are both negative (\\(\frac{-6}{10}\\) and \\(\frac{-6}{10}\\)).
• the ratios are both identical (\\(\frac{6}{10}\\) and \\(\frac{6}{10}\\)).

Explanation:

Find the sine ratio of angle x

Using the Sine Ratio knowledge point

$$ \sin(x^\circ) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{6}{10} $$

Find the cosine ratio of angle y

Using the Right Triangle Trigonometry knowledge point

$$ \cos(y^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{6}{10} $$

Compare the two ratios

Using the Cofunction Identities knowledge point

$$ \sin(x^\circ) = \cos(y^\circ) = \frac{6}{10} $$

Answer:

• The ratios are opposites (\(\frac{-6}{8}\) and \(\frac{6}{8}\))
• The ratios are reciprocals (\(\frac{6}{8}\) and \(\frac{8}{6}\))
• The ratios are both negative (\(\frac{-6}{10}\) and \(\frac{-6}{10}\))
• The ratios are both identical (\(\frac{6}{10}\) and \(\frac{6}{10}\)) (Correct answer)