Find trigonometric function values by hand? (sin, cos, tan)?

Question

I need to find the values of trigonometric functions (sin, cos, and tan) by hand without the use of a calculator. The values are all standard radian measures, such as -3pi/2 or 5pi/6. I know how the sin, cos, and tan values are derived (using "adjacent" "opposite" and "hypotenuse"). I don't understand how to graph the functions in a unit circle to find the values, though. Are there any websites that explain how this can be done? I can vaguely follow the textbook examples, but I don't understand it well enough to complete the problems on my own.

Thanks!

Answer 1

please clear your fundamental concept

sin(-x)= -sinx

os(-x)=cosx

now if x is more than 90 degree

then use the formulas for

sin (90+x)= cosx

all sin tan cos etc

Answer 2

well what i used to do is just split the given angle into two different angles whose sum leads to the given angle. though i think u mite feel this is a bit lengthy but i used to do it like this. for ex

5pi/6  =  (pi - pi/6)

ex.  sin(5pi/6)  =   sin(pi - pi/6)

                           sin(pi)cos(pi/6) - cos(pi)sin(pi/6)

                           0  -  (-1)(1/2)

                     =  1/2

i hope u atleast know the values of basic angles like sinpi/6 cos pi/3 etc.

Answer 3

the unit circle helps you "visualize" the values of cos, sin(theta) where theta is n*pi/6 or m*pi/4 where n and m are integers

each coordinate on the unit circle: (x,y) = (cos theta, sin theta)

where theta is your unit circle angle... examples: pi/6, pi/2, etc

so cos(-3pi/2) = cos pi/2 = 0  ... the angle -3pi/2 corresponds to unit circle coordinate (0,1)

similarly sin(5pi/6) = 1/2 ... the angle 5pi/6 corresponds to unit circle (-sqrt(3)/2,1/2)

where sqrt(n) denotes the square root of n

you can remember the values by "visualizing" which angle it is and its relation to the coordinates on the circle, and remembering that the coordinate values are a combination of 0, +/- 1,  +/-1/2, and  +/- sqrt(3)/2 and +/- sqrt(2)/2

where  +/- denotes either positive or negative value

Answer 4

use taylor series to approximately find your values for sin, cos, tan

Answer 5

In my day we had to use Log Books and Slide Rule - don't know how you would do it today manually.