Question

Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share?

Answer 1

Answer:

There are both on the same side of the image "O and P"

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Answer 2

Answer:

${a}^{2} + {b}^{2} = {c}^{2} \\ {8}^{2} + {6}^{2} = {c}^{2} \\ 64 + 36 = {c}^{2} \\ {c}^{2} = 100 \\ c = 10$

So; C is hypotenuse = 10

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sin x° = Opposite/hypotenuse

$sin \: x° = \frac{6}{10} \\ \\ sin \: x° = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}$

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cos y°= Adjacent/ hypotenuse

$cos \: y° = \frac{6}{10} \\ \\ cos \: y° = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}$

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$\frac{sin \: x°}{cos \: y°} = \frac{ \frac{3}{5} }{ \frac{3}{5} } = \frac{3}{5} \div \frac{3}{5} = \frac{3}{5} \times \frac{5}{3} = 1 \\ \\ \\ \frac{sin \: x°}{cos \: y°} = 1$