# How can I find the sine or the tan or the cos of an angle in radian?

There is an angle equal 0.54 radians and opposite leg equal to 3 units, I need to find the length of the adjacent leg. I know that I have to do ${\rm leg} = \frac{3}{\tan(0.54 \text{ rad})}$.

I got this task from books and there is the determination $0.54 \text{ rad} = \frac{3}{5}$ but there isn't any description how to get result from 0.54 radian to $\frac{3}{5}$. I tried to find $0.54 \text{ rad} = \frac{54}{100} = \frac{27}{50}$ but I couldn't do it. How can I get $\frac{3}{5}$ from 0.54 radian or from another number, for example 0.36? I found answer here, but I couldn't understand because I go to school and didn't find description such method in book my level

update I know answer, I understand solving, but I can't understand how to get $\frac{3}{5}$ from $0.54 \text{ rad}$.

• The tangent of an angle is equal to the opposite side divided by the adjacent side. Can you see how to get $\frac{3}{5}$ now? Dec 27, 2014 at 22:07
• 5 is the length of adjacent leg Dec 27, 2014 at 22:11
• @FlorianD'Souza, No. Dec 27, 2014 at 22:56
• To compute the sine, cosine, or tangent of an arbitrary angle by hand can be a long and laborious procedure. That is why they used to teach students how to look up the answer in a printed table of the functions--although or course someone else had to go to great trouble to create those tables. Are you asking about the details of such procedures? Dec 28, 2014 at 4:01
• @DavidK, yes, I know it is Taylor series Dec 28, 2014 at 18:01

$\tan(0.54)=0.5994..\approx \frac{3}{5}$ where the angle is in radian.

An approximation is the best you can do since $\tan(x) \not\in \mathbb{Q}$ if $x\ne0$ and $x \in \mathbb{Q}$ see this question and answers

• @Bot, sorry, I understood. thanks Dec 27, 2014 at 23:23

We know that one way to find the tangent of an angle is to divide the opposite side by the adjacent side. Therefore, we have:

$$\tan(0.54) = \frac{3}{x}$$ where x is the unknown length of the adjacent side. We can then solve for x:

$$x= \frac{3}{\tan(0.54)}$$ which is equal to 5.005 (approximately).

$\text{adjacent leg} = \frac{3}{tan(0.54rad)} = 5$

check

$$\tan^{-1}\left(\frac{3}{5}\right) = .54\text{rad}$$

//EDIT

CHECK

$5 * \tan(0.54\text{rad}) = 3$

because $5 * \frac{3}{5} = 3$

we can concluding that

$\tan(.54\text{rad}) = \frac{3}{5}$