# Exact Values of sin (theta)

1. Feb 10, 2010

### GreenPrint

1. The problem statement, all variables and given/known data

Does anyone know were I can find a table on the internet of the exact values of sin theta were theta is any whole angle from zero to ninety degrees

Example
sin 0 degrees
sin 1 degrees
sin 2
sin 3
sin 4
sin 5
...
sin 90

2. Relevant equations

3. The attempt at a solution

thank you i'm to lazy to calculate all of them on my own does anyone know where i could find a table I got about 10 of them done but don't want to waste hours of my llife calculating all 90 when they have already done so can some one point me in the right direction???

2. Feb 10, 2010

### CompuChip

Short answer: you already wrote down the exact values (they are sin(1o), sin(2o), etc.)

Long answer: only for a few special angles, we can write sin(x) in closed form, for example as $\frac{\pi}{a}$ for some integer a. In most cases, this is not possible. If you want a table of decimal values, you can use a program like Mathematica, for example
http://www.wolframalpha.com/input/?i=Table[N[Sin[x+Degree],+5],+{x,+0,+90}]

Note the use of the function N[..., 5] which gives the results in 5 decimals and compare this to the "exact" table
http://www.wolframalpha.com/input/?i=Table[Sin[x+Degree],+{x,+0,+90}]

3. Feb 10, 2010

### vela

Staff Emeritus
Do a web search for "trig table" and links to a bunch of nicely formatted tables will come up.

4. Feb 10, 2010

### willem2

Nice.

It seems they missed

$$sin \frac {\pi}{20} = \sqrt { \frac {1-\sqrt { \frac {5}{8} + \frac {\sqrt {5}}{8}}} {2}}$$

however and some more multiples of 9 degrees.

5. Feb 10, 2010

### CompuChip

However, there is

sin(pi/20) = 1/2 * (-1)^(9/20) * (-1 + (-1)^(1/10))

6. Feb 10, 2010

### dacruick

use any computer program. then go y = sin(x)
then say x = 0.

while x<91
y=sin(x)
print y
x+=1