Question

question 8 (1 point)
\t△pqr has a right angle at q. if q = 26 cm and p = 10 cm, which of the following is the correct set of reciprocal trigonometric ratios for ∠r?
\t\t○ a)
\t\t\tcsc r = 12/13, sec r = 5/13,
\t\t\tcot r = 12/5
\t\t○ b)
\t\t\tcsc r = 13/5, sec r = 13/12,
\t\t\tcot r = 5/12
\t\t○ c)
\t\t\tcsc r = 13/12, sec r = 13/5,
\t\t\tcot r = 5/12
\t\t○ d)
\t\t\tcsc r = 13/12, sec r = 13/5,
\t\t\tcot r = 12/5

Explanation:

Step1: Find the length of side \( r \)

Using the Pythagorean theorem \( q^{2}=p^{2}+r^{2} \). Given \( q = 26\) cm and \( p = 10\) cm.

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Step2: Recall the reciprocal trigonometric ratios

• \(\csc R=\frac{q}{r}\) (since \(\sin R=\frac{r}{q}\)), \(\sec R=\frac{q}{p}\) (since \(\cos R=\frac{p}{q}\)), \(\cot R=\frac{p}{r}\) (since \(\tan R=\frac{r}{p}\))
• Substitute \(q = 26\), \(p = 10\), \(r = 24\)

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Answer:

C. \(\csc R=\frac{13}{12},\sec R=\frac{13}{5},\cot R=\frac{5}{12}\)