# Expressing a decimal number in radians in terms of pi in a fraction

#### JFonseka

1. Homework Statement

arctan(sin((3 / 4) * pi) * 2) = 0.955316618

I want to express that in terms of a fraction with reference to pi.

3. The Attempt at a Solution

I thought of first dividing that by pi itself, and then convert the resulting number into a fraction and tack pi on at the end, but the calculator won't convert the number.

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#### SteamKing

Staff Emeritus
Homework Helper
Get a calculator that works.

#### JFonseka

Yes, thank you for your valuable contribution. Go do something that's more constructive than wasting time irritating others with useless answers.

#### tiny-tim

Homework Helper
… the calculator won't convert the number.
the calculator won't convert what number to what?

#### JFonseka

On scientific calculators there is that fraction button that converts decimal numbers to fractions, however for this particular number it won't do it, either because it needs more decimal places to figure out a proper fraction or because it's not possible at all. It's part of a question from a past paper, so I'm assuming they want the answer in a fraction form of pi.

#### HallsofIvy

Homework Helper
$$\frac{0.955316618}{\pi}= 0.30408672$$
$$0.30408672= \frac{30408672}{100000000}$$

so
$$0.955316618= \frac{3040867}{100000000}\pi$$

That fraction can be reduced of course.

#### tiny-tim

Homework Helper
On scientific calculators there is that fraction button that converts decimal numbers to fractions
i've never heard of that

so if you entered π (3.14159), and pressed the button, what should it give … 22/7 ?
… It's part of a question from a past paper, so I'm assuming they want the answer in a fraction form of pi.
why??

#### SPYazdani

i've never heard of that

so if you entered π (3.14159), and pressed the button, what should it give … 22/7 ?

why??
Probably to prove that OP understands the concept in an upcoming exam because giving a decimal answer is proof enough of using a prohibited calculator

#### JFonseka

tinytim thanks for your answer, though it's confusing I got that exact same fraction using an online calculator but that answer seems weird for an exam question.

And no, typing 3.14159 won't make it 22/7, because it's not exactly that.

Suppose there was some answer that came out to something like 0.210526315, and I pressed the fraction button, it would convert it to 4/19. I'm not too sure of the exact mechanics, it's just a button I've been familiar with for a while.

As for why they want it like that, it's just a standardized format. The full question was

Let a = 2e^(3*pi*i/4)

Plot a and the conjugate of a on the Argand diagram indicating the modulus and principal argument. I was working on getting the angle for the conjugate, which is that 0.955...number, but since the angles are usually expressed in some variation of a fractional pi, I was trying to convert that.

As for what SPYazdani said:

Probably to prove that OP understands the concept in an upcoming exam because giving a decimal answer is proof enough of using a prohibited calculator
I'm not too sure what you're trying to imply here. However it has nothing to do with prohibited calculators, it's an approved calculator and probably an outdated one at that. I'm working on a maths subject I completed nearly 4 years ago, and am revising it because I started university again and can't remember a thing, just to clear things up, and it has nothing to do with any upcoming exams.

#### tiny-tim

Homework Helper
Hi JFonseka!
The full question was

Let a = 2e^(3*pi*i/4)

Plot a and the conjugate of a on the Argand diagram indicating the modulus and principal argument. I was working on getting the angle for the conjugate, which is that 0.955...number, but since the angles are usually expressed in some variation of a fractional pi, I was trying to convert that.
stop making things difficult for yourself!

"indicating the … principal argument" is asking for an angle, nothing more …

you can give it in units of radian or degree

(and only convenient angles, such as 45° or 30°, are usually expressed as a multiple of π)

#### JFonseka

Hey tiny-tim,

Thanks a lot for your time and help with my problem =)

Cheers

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