Given that cos xo = \(\frac{1}{r}\), express tan x in terms of r

Mathematics

WAEC 2011

Given that cos x^o = \(\frac{1}{r}\), express tan x in terms of r

A. \(\frac{1}{\sqrt{r}}\)
B. \(\sqrt{r}\)
C. \(\sqrt{r^2 + 1}\)
D. \(\sqrt{r^2 - 1}\)

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Correct Answer: Option D

Explanation

cos x^o = \(\frac{1}{r}\); \(\sqrt{r^2 - 1}\)

By Pythagoras r² = 1² + x² - 1

x = \(\sqrt{r^2 - 1}\)

tan x^o = \(\sqrt{r^2 - 1}\)

= \(\sqrt{r^2 - 1}\)

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Given that cos xo = \(\frac{1}{r}\), express tan x in terms of r

Correct Answer: Option D

Explanation

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