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sin cos tan





ParsaAkbari
May i ask what are the values of sin cos and tan, also sin-1 cos-1 and tan-1

If somebody wanted to make a trigonamatry "calculator" where you enter your values and it does all the working out for you, what would the variable sin cos tan be? (also sin-1 cos-1 tan-1)
TomS




tan(x) = sin(x) / cos(x)
Afaceinthematrix
I do not understand your question. What do you mean, "what are the values of sin cos and tan, also sin-1 cos-1 and tan-1?"

Trig functions don't have "values" like constants (such as Pi and e). Sin(pi) will equal 0, but so will Sin(kPi), with k being an integer. Sine and Cosine are both ratios, with Tangent being equal to Sin/Cos.

As far as arctan, arcsin, and arccos (arccos is the same as cos-1), that's simply the inverse, replace x and y. For instance, the value of arccos(1) will be 0 because cos(0)=1. Does that help any? I'm terrible at teaching and even worse at doing it online in text.
Xanatos
Alternatively

e^ix=Cos(x) + iSin(x)

so Cos is the real part of e^ix and Sin is the imaginary part of e^ix
infinisa
Hi ParsaAkbari

If you want to see efficient ways to calculate trig functions, I suggest you take a look at the links on this paragraph of the Wiki article on Trigonometric functions:

Modern computers use a variety of techniques.[5] One common method, especially on higher-end processors with floating point units, is to combine a polynomial or rational approximation (such as Chebyshev approximation, best uniform approximation, and Padé approximation, and typically for higher or variable precisions, Taylor and Laurent series) with range reduction and a table lookup — they first look up the closest angle in a small table, and then use the polynomial to compute the correction.[6] On devices that lack hardware multipliers, an algorithm called CORDIC (as well as related techniques) which uses only addition, subtraction, bitshift and table lookup, is often used. All of these methods are commonly implemented in hardware floating point units for performance reasons.

For very high precision calculations, when series expansion convergence becomes too slow, trigonometric functions can be approximated by the arithmetic-geometric mean, which itself approximates the trigonometric function by the (complex) elliptic integral.[7]


Hope this is useful
Kaseas
Xanatos wrote:
Alternatively

e^ix=Cos(x) + iSin(x)

so Cos is the real part of e^ix and Sin is the imaginary part of e^ix


Throwing euler's identity at him doesn't help any...
Afaceinthematrix
Xanatos wrote:
Alternatively

e^ix=Cos(x) + iSin(x)

so Cos is the real part of e^ix and Sin is the imaginary part of e^ix


Well if you're going to throw something like that at him (which will most likely confuse someone new to trig), you might as well just throw the Taylor Series at him/her.

Sin(X) = (((-1)^n)x^(2n+1))/(2n+1)!

Cos(X) = (((-1)^n)x^(2n))/(2n)!
SonLight
I once tried to think of a simple way to explain the trig functions without using ideas from higher math. First of all, you need to know that they are not simply a single value. For every angle, there is a unique number between -1 and 1 which is its sine. Sine is the actual name of the function, but mathematicians like to shorten it to sin so they can write something like sin(45 degrees) = .707 or sin(90 degrees) = 1.

Consider the sine function to be the "closing door" function. When the door is fully open ( 0 degrees ) the apparent width of the door is zero, since you view it edge-on. When the door is half closed ( 45 degrees ) you might think the apparent width of the door would be 1/2 the full width, but if you try it you will see that it's a bit more than that, in fact slightly more than 7/10 the full width of the door, When the door is fully closed, you see the full width of the door. So we have sin(0) = 0, sin(45) = .707, and sin(90) = 1. I can explain how the cosiine (or cos) is the "opening door" function, starting at 1, if you haven't gone to sleep yet. Sin-1 of course means "the angle whose sin is" whatever number is plugged into the function.
ashgray2
Great Ideas! I love reading this post. Sin cos tan I love mathematics.
slashnburn99
Wiki for me

got to say Pi is about the furthset i get to regularly

Sin Cos and Tan just buttons on calculator Very Happy
guissmo
Make a circle of radius 1. Mark the center of the circle as the origin (0,0).

The number right after sin, cos, tan (i.e. pi or pi/2) is an angle.
Angle 0 is the right-most part of the circle. pi/2 is the top. pi is to the left and 3pi/2 is to the right.
Just think of it as incrementing by pi/2 for every 90 degrees.

Now, sin stands for the "y" coordinate and cos stands for the "x" coordinate.
So when I ask you what cos(pi/2) is, you tell me the x-coordinate of cos(pi/2). Which is 0.

Tan on the other hand is just sin/cos. I think there's a graphical explanation for tangent, but I can't remember what it was.

Hope this helps.
cabenqc
If someone asked me such questions 40 or more years ago.
I think my answer is, get a "4 figures table" or "7 figures table".

Today, if you just want to get the numeric value of those trigonometrical functions,
use a scientific calculator or spreadsheet such as excel.

Hope this helps.
cabenqc
Me again.
I read your post again after my last reply.

I guess you're talk about how to calculate those numeric values using computation with those function available.
Yes, those above replies is the correct way to calculate such values.

For me, if I need to calculate such trigonometrical function numeric values,
I use "Numerical Recipes" to do that.
Numerical Recipes Home Page
http://www.nr.com
http://www.nr.com/oldverswitcher.html

Hope this helps.
cabenqc
sorry my typo:

I guess you're talk about how to calculate those numeric values using computation
[with] WITHOUT
those function available.
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