Given that cos x o = 1/r, express tan x in terms of r

Correct Answer is : r2−1{r² - 1}r2−1

Correct Answer is : r2−1{r² - 1}r2−1

Test Index

WAEC Mathematics 2011 Paper

Question : 3

Total: 47

\frac{1}{r}

, express tan x in terms of r

Solution:

Concept:

Use a right-angled triangle to relate

\cos x

and

\tan x

Explanation:

Given

\cos x^\circ = \frac{1}{r}

In a right triangle,

\cos x^\circ = \frac{\text{adjacent}}{\text{hypotenuse}}

So take adjacent side

= 1

and hypotenuse

= r

Using Pythagoras theorem:

r^2 = 1^2 + (\text{opposite})^2

\text{opposite} = \sqrt{r^2 - 1}

Now

\tan x^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sqrt{r^2 - 1}}{1}

Therefore,

\tan x^\circ = \sqrt{r^2 - 1}

Answer:

\sqrt{r^2 - 1}

, which is option D.

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