Hi, How can I compute the trigonometric functions such as Sine, Cosine and Tangent?

Question

Hi, how can I compute the trigonometric functions like, Sine, Cosine and Tangent, without using a calculator. I mean by pencil and hand ?

Answer 1

SOH CAH TOA. Sine: Opposite/Hypotenuse. Cosine: Adjacent/Hypotenuse. Tangent: Opposite/Adjacent.

Answer 2

For the sine cosine tangent and exponent there are maclaurin expansions that are true for all values of the variable.
To derive consider for example,
sin x = a0 + a1x + a2x^2 +....+arx^r +....ad infinitum
using x=0 gives a0 , differentiating the whole series and again using x=0 gives a1 etc.
Similarly for other circular functions.
Now use the series and substitute the required value for an approximation.

Answer 3

(If you do not have a real scientific calculator, you can switch the built-in MS-Windows-calculator from standard to scientific view and calculate the trigonometric fungtions up to 32 digits, very precisely.)

If you really want to do it with pencil and paper, you can do it with the Taylor-row:
sin(x) = x -x^3/3! +x^5/5! -x^7/7! +...
cos(x) = 1 -x^2/2 +x^4/4! -x^6/6! +...
tan(x) = x +1/3x^3 +2/15x^5 +17/315x^7 +...

( x is in radians and needs to be small to have the answer quickly! :-)
( x^3 = x*x*x and 5! = 1*2*3*4*5 ) Good luck and have fun! Kay

Answer 4

To *compute* a trigonometric function (rather than try to measure from a drawing), you can use a polynomial approximation of the function---such as a partial sum of the Taylor series. This reduces the task to arithmetic. (It can be further reduced to pure addition by the method of finite differences. This was an application envisaged by Babbage for his difference engine.)

Answer 5

Draw a right-angled triangle with sides, AB, BC and AC as its hipotenus. Let the assumed angle BAC.
sine BAC = BC/AC
cosine BAC = AB/AC
tangent BAC = BC/AC

Answer 6

draw unit circle (radius is 1) with cordinates
(1,0) is 0 first value is cos and second value is sin. divide it u get tan
(0,1) is pi/2
(-1,0) is pi
(0,-1) is 3*pi/2
and so on