Chapter 2, Problem 1RE

To determine

To calculate: The trigonometric function of the expression $\frac{\cos x}{\sin x}$.

Answer to Problem 1RE

The trigonometric function of the expression $\frac{\cos x}{\sin x}$ is $\cot x$.

Explanation of Solution

Calculation:

Consider the expression, $\frac{\cos x}{\sin x}$.

Now, from the trigonometric formula,

$\sin x=\frac{\text{opp}}{\text{hyp}}$ …… (1)

And,

$\cos x=\frac{\text{adj}}{\text{hyp}}$ …… (2)

Divide equation (2) by equation (1),

$\begin{array}{c}\frac{\cos x}{\sin x}=\frac{\frac{\text{adj}}{\text{hyp}}}{\frac{\text{opp}}{\text{hyp}}}\\ =\frac{\text{adj}}{\cancel{\text{hyp}}}\cdot \frac{\cancel{\text{hyp}}}{\text{opp}}\\ =\frac{\text{adj}}{\text{opp}}\end{array}$

So,

$\frac{\cos x}{\sin x}=\frac{\text{adj}}{\text{opp}}$ …… (3)

Since, from the trigonometry formula,

$\cot x=\frac{\text{adj}}{\text{opp}}$ …… (4)

From equation (3) and (4),

$\frac{\cos x}{\sin x}=\cot x$

Therefore, the trigonometric function of the expression $\frac{\cos x}{\sin x}$ is $\cot x$.