Question about Texas Instruments TI-83 Plus Calculator
I keep getting wrong answers with the radians mode on. What i typed in was cos(20π + (π/2)) and I get a weird answer (-1E-13) when i know the answer should be zero because i did it on another calculater and that's what i got. Please help me, i have no idea what could be wrong because with other specific things (sin( 20π + (π/2)) for example) ive typed in it does give the right answer, but i don't know why with the other one it doesn't.
-1E-13 is a very small number. When doing this kind of a problem you can regard 1E-13 as 0.
Remember that pi is an irrational number. It is only estimated on your calculator. I just played around with a TI-83 and found the following answers:
cos(pi/2) = 0
cos(2*pi + pi/2) = 0
cos(4*pi + pi/2) = 1E-13
cos(20*pi + pi/2) = -1E-13
As you know, that correct answer to each of these is 0. The calculator gives non-zero answers because some very small errors are accumulating. There is nothing wrong with your calculator.
Posted on Nov 20, 2007
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Posted on Jan 02, 2017
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Mar 25, 2014 | Casio FX-115ES Scientific Calculator
Let's start with a little background.
The cot(x) is also known as the cotangent(x) and it equals 1/tan(x) which equals cos(x)/sin(x). I'm showing these formulas because your calculator may not have a cot button but it will probably have buttons for tan, cos, and sin.
Your calculator may also have buttons for tan-1, cos-1 and sin-1. These are the inverse functions for tan, cos, and sin. If you enter a number and then push the tan-1 button, the result is the angle whose tangent is the entered number. For example, it you enter 1 and push the tan-1 button the answer will be 45 deg because tan (45 deg) = 1.
Now let's look at the problem, cot(x) = -0.6.
The first thing we need to know is do you want the answer in degrees or radians? Your calculator will have both modes. The default mode when you first turn it on is probably degrees. If this problem is in radians you will need to change the mode of your calculator over to radians before we start.
If cot(x) = -0.6, then tan(x) = 1/-0.6 from the formula I showed in the background section.
This means tan(x) = -1.6666666...
Now we just enter -1.66666667 and hit the tan-1 button to get the answer.
If we're operating in radians the answer is -1.0307 radians.
If we're operating in degrees the answer is -59.036 deg.
I hope this helps you out.
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