finding the values of the other trigo functions given one function?

(note: In your two problems, you have angle A…. for explanation purposes, I call your angle A “Angle N” instead…. because I have “A” representing the adjacent leg of the right triangle… and it will get too confusing if we have A’s representing two different things… okay?)

Anyways, do you remember SOH CAH TOA? That means…

Sin(angle N) = opposite leg/ hypoteneuse OR Sin ang = O/H

Cos(angle N) = adjacent leg / hypoteneuse OR Cos ang = A/H

Tan(angle N) = opposite leg / adjacent leg OR Tan ang = O/A

Cot(angle N)=1/TanA = reciprocal of Tan(angle) OR Cot ang = A/O

……..__ ,,._

………/../.| |

…….././…| |

……././….| |

…..H./…..| O

….././……| |

…././…….| |

…/./……..| |

.././………| |

././)N___r|.v_

|<-- A -->|

PROBLEM 1: Sin (ang N) = 4/5…

You know Sin(angle N) = O/H

You know O = 4 and H = 5…. therefore you have a 3/4/5 right triangle… and now you know that the adjacent side (A) is 3

……..__ ,,._

………/../.| |

…….././…| |

……././….| |

…..5./…..| 4

….././……| |

…././…….| |

…/./……..| |

.././………| |

././)N___r|.v_

|<-- 3 -->|

So…

sin N = 4/5, cos N = 3/5, tan N = 4/3, csc N = 5/4, sec N = 5/3, and Cot ang = 3/4

______________________________

PROBLEM 2:

Remember what I said above?

Tan(angle) = opposite leg / adjacent leg OR Tan ang = O/A

Cot(angle) = 1/TanA = reciprocal of Tan(angle) OR Cot ang = A/O

So here you are given Cot ang = a/b…

That means that Tan ang is the reciprocal of Cot ang…

So… knowing Cot ang = a/b… you also know that Tan ang = b/a… (the reciprocal of Cot ang…)

So you know that O = b and A = a…

Since your two sides of the triangle that form the right angle… are “a” and “b”…. let’s let “c” represent the hyptoneuse of the right triangle…. Okay?

so we have …

……..__ ,,._

………/../.| |

…….././…| |

……././….| |

…..c./…..| b

….././……| |

…././…….| |

…/./……..| |

.././………| |

././)N___r|.v_

|<-- a -->|

sin N = b/c, cos N = a/c, tan N = b/a, csc N = c/b, sec N = c/a, and cot N = a/b