# Simple algebra/trig expression, need help simplifying

## Main Question or Discussion Point

Hello, I'm trying to solve this equation.

(4-4cos(∏*0.16*4)) - (4-4cos(∏*0.16*3))

It seems like it should be so easy. First I start with the left hand side (∏*0.16*4). Then I take the cosine of that, and then multiply it by 4. Then I do 4 - [answer] to get a value for the full left side (0.00246263391564268270661821942049).

Then I do the same thing with the right side. (∏*0.16*3) and take the cosine of that. Multiply it by 4 and subtract that answer from 4 for a right side value of 0.00138529377181347385337035623753.

Then I subtract the right side from the left side..

0.00246263391564268270661821942049 - 0.00138529377181347385337035623753 = 0.00107734014382920885324786318296

But this is far from the right answer, which is supposed to be roughly 1.95. I don't know what I'm doing wrong. I've tried degrees, radians, gradients. I've tried changing the order in which I multiply everything but nothing seems to get me to the right answer. Even wolfram alpha tells me the right answer, but it doesn't explain HOW it gets that answer. image hosting

I'm going crazy because I can't figure this out. I suspect that I'm not processing cosine right somehow, but I really have no idea what the right way should be. I thought it is just the cosine of the product of everything in the parenthesis.

I don't think it's a calculator error. I'm mainly using the calculator on Windows 7 but I tried it also on a handheld calculator and still get the same answer.

You have your calculator(s) set to degrees (it's assuming the arguments of cosine and sine are in degrees), whereas WolframAlpha (and most likely the original problem) assumes them to be radians.

Explicitly stating the arguments to be degrees yields ~.00108 in WolframAlpha.

• 1 person
Ughhh, thank you so much. I swear I tried it in radians and it didn't come out right. I must have just made a computational error when I did it. But I just did it again and it works. I feel so stupid now, but thank you so much.

No problem :]

Mark44
Mentor
Hello, I'm trying to solve this equation.

(4-4cos(∏*0.16*4)) - (4-4cos(∏*0.16*3))
No, you're not. This isn't an equation since it doesn't have = in it. What you're doing is evaluating this expression.
It seems like it should be so easy. First I start with the left hand side (∏*0.16*4).
Be careful with your terminology. "Left side" and "right side" normally refer to the left and right side of an equation.
Then I take the cosine of that, and then multiply it by 4. Then I do 4 - [answer] to get a value for the full left side (0.00246263391564268270661821942049).
It would be useful (and helpful) to do some simplification first.

$4 - 4cos(\pi * .16 * 4) - (4 - 4cos(\pi * .16 * 3))$
$= 4 - 4cos(.64\pi) - 4 + 4cos(.48\pi)$
$= - 4cos(.64\pi) + 4cos(.48\pi)$
Then I do the same thing with the right side. (∏*0.16*3) and take the cosine of that. Multiply it by 4 and subtract that answer from 4 for a right side value of 0.00138529377181347385337035623753.

Then I subtract the right side from the left side..

0.00246263391564268270661821942049 - 0.00138529377181347385337035623753 = 0.00107734014382920885324786318296

But this is far from the right answer, which is supposed to be roughly 1.95. I don't know what I'm doing wrong. I've tried degrees, radians, gradients. I've tried changing the order in which I multiply everything but nothing seems to get me to the right answer. Even wolfram alpha tells me the right answer, but it doesn't explain HOW it gets that answer. image hosting

I'm going crazy because I can't figure this out. I suspect that I'm not processing cosine right somehow, but I really have no idea what the right way should be. I thought it is just the cosine of the product of everything in the parenthesis.

I don't think it's a calculator error. I'm mainly using the calculator on Windows 7 but I tried it also on a handheld calculator and still get the same answer.

No, you're not. This isn't an equation since it doesn't have = in it. What you're doing is evaluating this expression.
Honestly I meant to write expression. Guess I was too caught up in just getting the problem out there. But thanks.

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