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

• JFonseka
In summary, the conversation discusses a method for expressing the value of arctan(sin((3/4)*pi)*2) in terms of a fraction with reference to pi. The suggestion is to divide the value by pi and convert the resulting number into a fraction, but the calculator does not convert the number. The use of a fraction button on scientific calculators is mentioned, and the reason for wanting the answer in a fraction form of pi is discussed. The original poster is working on revising a maths subject and is seeking clarification for an upcoming exam. Another user suggests that it is unnecessary to convert the value to a fraction and that giving the angle in units of radians or degrees is sufficient. The conversation ends with the original poster thanking the other
JFonseka

## Homework Statement

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

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

## 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.

Get a calculator that works.

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

JFonseka said:
… the calculator won't convert the number.

the calculator won't convert what number to what?

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.

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

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

That fraction can be reduced of course.

JFonseka said:
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??

tiny-tim said:
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

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.

Hi JFonseka!
JFonseka said:
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)

Hey tiny-tim,

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

Cheers

## 1. How do you convert a decimal number to radians in terms of pi?

To convert a decimal number to radians in terms of pi, simply divide the decimal by pi. The resulting quotient will be the number of radians in terms of pi.

## 2. Can you provide an example of expressing a decimal number in radians in terms of pi in a fraction?

Sure. For example, if we have the decimal number 0.75, we can express it in radians in terms of pi as 3π/4. This means that 0.75 is equivalent to 3/4 of a full circle, which is represented by 2π radians.

## 3. What is the significance of expressing radians in terms of pi?

Expressing radians in terms of pi allows us to easily compare and convert between different units of angle measurement, such as degrees and radians. It also allows us to represent fractions of a full circle in a concise and standardized way.

## 4. Is it possible to have a decimal number of radians in terms of pi?

Yes, it is possible to have a decimal number of radians in terms of pi. For example, 0.5 radians is equivalent to π/2. This means that the decimal 0.5 represents half of a full circle, which is represented by π radians.

## 5. Can you convert a fraction of radians to a decimal in terms of pi?

Yes, you can convert a fraction of radians to a decimal in terms of pi by multiplying the fraction by pi. For example, if we have 3π/4, we can convert it to a decimal by multiplying 3/4 by pi, which gives us the decimal 0.75.

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