First of all we start with the formulas.

sin(a + b) =
sin(a)cos(b) + cos(a)sin(b)

sin(a - b) =
sin(a)cos(b) - cos(a)sin(b)

cos(a + b) =
cos(a)cos(b) - sin(a)sin(b)

cos(a - b) =
cos(a)cos(b) + sin(a)sin(b)

Next, we give you a table of sine and cosine values.

Angle | sin | cos | Angle | sin | cos |
---|---|---|---|---|---|

1^{o} |
0.0175 | 0.9998 | 2^{o} |
0.0349 | 0.9994 |

3^{o} |
0.0523 | 0.9986 | 4^{o} |
0.0698 | 0.9976 |

5^{o} |
0.0872 | 0.9962 | 6^{o} |
0.1045 | 0.9945 |

7^{o} |
0.1219 | 0.9925 | 8^{o} |
0.1392 | 0.9903 |

9^{o} |
0.1564 | 0.9877 | 10^{o} |
0.1736 | 0.9848 |

20^{o} |
0.3420 | 0.9397 | 30^{o} |
0.5000 | 0.8660 |

40^{o} |
0.6428 | 0.7660 |

**Example 1:** Find sin(45^{o}).

sin(45) = sin(40 + 5)

= sin(40)cos(5) + cos(40)sin(5)

= (0.6428)(0.9962) + (0.766)(0.9872)

= 0.7071

**Example 2:** Find cos(45^{o}).

cos(45) = cos(40 + 5)

= cos(40)cos(5) - sin(40)sin(5)

= (0.766)(0.9962) - (0.6428)(0.9872)

= 0.7071

The observant ones among you would have noticed that the angles only
go up to 40^{o}. That's because we can take advantage of the
fact that sin(90) = 1 and cos(90) = 0.

**Example 3:** Find sin(75^{o}).

sin(75) = sin(90 - 15)

= sin(90)cos(15) + cos(90)sin(15)

= cos(15)

**Example 4:** Find cos(75^{o}).

cos(75) = cos(90 - 15)

= cos(90)cos(15) + sin(90)sin(15)

= sin(15)

This should be apparent if you draw a right-angle triangle with the
angles of 15^{o} and 75^{o}. If you need a refresher on
the basics of trig, check out the
basic trigonometry facts page.

There are also trig identities involving the sum angle formulas.

Copyright © 2011 - Mathwizz.com all rights reserved