How to get exact numbers on the calculator?

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HollowPointSmile
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I was doing some questions on trig which ask for exact numbers, but when I work it out I get my answer in decimals and not surds. Do I need to change the mode or something? ]

Its a typical casio calculator.

Thanks in advance
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HollowPointSmile
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Guru Jason
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Put your calculator back into radons instead of degrees I think. Not sure how this is done though. I think it might be the 2nd Funtion button.
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claret_n_blue
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What's a "typical casio calculator"? Mine is a Casio fx-83GT and it has a "math" mode which you can put the calculator into and it gives you the answers in exact form.
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Kidneyjean
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It may not be possible to write the answer to your question as a surd...

But for everything else, there's the S<=>D button! It's just above the DEL key on my calculator, and all the Casio models seem to be pretty similar.

(the button converts fractions/surds into decimals, and back again)
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lukas1051
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If you have one with 'textbook display' which I assume you do, trying resetting it, it might be in a weird mode. If you're doing trig it could be in the wrong mode as someone else said (degrees vs radians). If not, maybe your calculator just doesn't do it :dontknow:
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HollowPointSmile
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(Original post by claret_n_blue)
What's a "typical casio calculator"? Mine is a Casio fx-83GT and it has a "math" mode which you can put the calculator into and it gives you the answers in exact form.
Thats the one I have, I'll try and switch the mode. The problem isn't do to with radians or degrees.
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TenOfThem
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I assume that, if the answer is required as an exact number then the angles used will be 30, 45, 60, 90, or multiples of these, or sums/differences of these and that a calculator is not expected

Could you give some exapmles
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claret_n_blue
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(Original post by HollowPointSmile)
Thats the one I have, I'll try and switch the mode. The problem isn't do to with radians or degrees.
Do:

- Shift + Mode
- Press Number 1 (to select the "MthIO" thing)
- Press Number 1 again (to confirm this)

Then check by just typing in root 2 or something
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v2p
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(Original post by HollowPointSmile)
I was doing some questions on trig which ask for exact numbers, but when I work it out I get my answer in decimals and not surds. Do I need to change the mode or something? ]

Its a typical casio calculator.

Thanks in advance
Sometimes when questions ask for exact number answers, its intentionally wanting you not to use a calculator to solve the question.

For example you could have a quadratic equation where you need to solve to find the exact answers to the two solutions. You could just solve it using the calculator solve thing (if you have it on yours, not sure which casio you have), and that might give you the two solutions as being numbers with loads of decimal points. Instead the question is looking to see if you can complete the square, which will give you the 'exact answers' to the two solutions.
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HollowPointSmile
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The question is :

Given that cosA = 3/4, where 270< A <360, find the exact value of sin2A.

The answer they get for sinA, as the exact value is sinA=- (7)/4 (the 7 is in a square root)
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TenOfThem
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No calculator required for this question

Pythagoras tells us the value of sinA

sin2A can be found using cosA and sinA


As I say ... this is a non-calculator question and that is what I would generally expect when the question asks for the exact answer
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ttoby
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(Original post by HollowPointSmile)
The question is :

Given that cosA = 3/4, where 270&lt; A &lt;360, find the exact value of sin2A.

The answer they get for sinA, as the exact value is sinA=- (7)/4 (the 7 is in a square root)
Here, they want you to use sin2A = 2sinAcosA.

cosA you already know, and sinA can be obtained using sin^2 A = cos^2 A = 1. Notice that you get a plus/minus come in when you do the square root. This is where you make use of 270< A <360 to determine if sinA should be positive or negative.
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HollowPointSmile
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(Original post by TenOfThem)
No calculator required for this question

Pythagoras tells us the value of sinA

sin2A can be found using cosA and sinA


As I say ... this is a non-calculator question and that is what I would generally expect when the question asks for the exact answer
The value I get for sinA is 3/5....
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ttoby
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(Original post by HollowPointSmile)
The value I get for sinA is 3/5....
You must have made a mistake somewhere. Post your workings so we can see where you went wrong.
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TenOfThem
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(Original post by HollowPointSmile)
The value I get for sinA is 3/5....
Not sure how

Since Cos is A/H and Sin is O/H they have to have the same denominator
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pwcroberts
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(Original post by HollowPointSmile)
The value I get for sinA is 3/5....
That is correct. but often when they mean exact numbers it will be using one of the angles that you should know of 30, 45 60
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ttoby
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(Original post by pwcroberts)
That is correct.
No it isn't.
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PrinceyJ
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(Original post by pwcroberts)
That is correct. but often when they mean exact numbers it will be using one of the angles that you should know of 30, 45 60
What you mean is.. you'll either get integers or rational numbers. But exact number is just the raw numerical value (recurring decimals if irrational).
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ttoby
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(Original post by PrinceyJ)
What you mean is.. you'll either get integers or rational numbers. But exact number is just the raw numerical value (recurring decimals if irrational).
If you're giving an exact number, you wouldn't leave an irrational number in decimal format since that would require you to round it somewhere and it wouldn't be exact.

'Exact answer' basically means giving the answer as a surd, or fraction, or in terms of e or pi as appropriate.
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