Question

if \\(\sin y^\circ = \frac{s}{8}\\) and \\(\tan y^\circ = \frac{s}{t}\\), what is the value of \\(\sec y^\circ\\)? (4 points)

\\(\sec y^\circ = 8s\\)
\\(\sec y^\circ = 8t\\)
\\(\sec y^\circ = \frac{8}{t}\\)
\\(\sec y^\circ = \frac{t}{8}\\)

Explanation:

Relate tangent, sine, and cosine ratios

$$ \tan y^\circ = \frac{\sin y^\circ}{\cos y^\circ} \implies \cos y^\circ = \frac{\sin y^\circ}{\tan y^\circ} $$

Substitute the given values

$$ \cos y^\circ = \frac{\frac{s}{8}}{\frac{s}{t}} = \frac{s}{8} \cdot \frac{t}{s} = \frac{t}{8} $$

Find the secant ratio

$$ \sec y^\circ = \frac{1}{\cos y^\circ} = \frac{8}{t} $$

Answer:

• \(\sec y^\circ = 8s\)
• \(\sec y^\circ = 8t\)
• \(\sec y^\circ = \frac{8}{t}\) (Correct answer)
• \(\sec y^\circ = \frac{t}{8}\)