Question

If $\tan x = .88$, what is $\cot x$ ?

Answer 1

Hint: Here we have the value of $\tan x$ and we have to find the value of $\cot x$ which we can find out by using a trigonometric formula. The formula which is to be used is $\cot x = \dfrac{1}{{\tan x}}$ . It is a simple substitution formula problem.

Complete step by step answer:
The given value of $\tan x = .88$ i.e., $\tan x = 0.88$ because if no number is given before decimal, we assume it to be $0$.

Now to find $\cot x$, we use the following formula,
$\cot x = \dfrac{1}{{\tan x}}$
Substituting the given value of $\tan x$,
$\cot x = \dfrac{1}{{0.88}}$
We can write $0.88$ as $\dfrac{{88}}{{100}}$,
$\cot x = \dfrac{1}{{\dfrac{{88}}{{100}}}}$
Taking $100$ to the numerator,
$\cot x = \dfrac{{100}}{{88}}$
Dividing the numbers, we get,
$\cot x = 1.136$

Therefore, we get the value of $\cot x = 1.136$ .

Note:
$\tan x$ is the reciprocal of $\cot x$ i.e., the product of $\tan x$ and $\cot x$ is always $1$. In the above problem, we assume the number before decimal to be $0$ as there is no other number before decimal and the significance of $0$ before decimal is as good as no number. If $\sin x$ value was given and we were asked to find the value of $\cos ecx$, there also we will use the same concept. $\sin x$ is the reciprocal of $\cos ecx$ and their product is $1$ .