## Class Details

- Class Name:
- Trigonometry: Sine, Cosine, Tangent 211
- Difficulty:
- Intermediate
- Number of Lessons:
- 18

## Class Outline

- Right Triangle Relationships
- Labeling Right Triangles
- Sine, Cosine, and Tangent
- SOHCAHTOA
- Triangles and Trigonometric Ratios Review
- Sine: Finding a Missing Dimension
- Cosine: Finding a Missing Dimension
- Trigonometry Calculator
- Tangent: Finding a Missing Dimension
- Finding a Missing Angle
- Finding Unknowns Using Trigonometric Ratios Review
- Cosecant, Secant, and Cotangent
- Finding Dimensions Using Less Common Ratios
- Tapers
- Calculating Taper per Foot
- Finding a Taper Angle: Sample Problem
- Finding a Taper Angle: Sample Problem #2
- Less Common Ratios and Tapers Review

## Objectives

- Describe the relationship between the sides and angles of a right triangle.
- Label the sides of a right triangle according to its reference angle.
- List the most common trigonometric ratios.
- Explain the phrase SOHCAHTOA.
- Solve for a missing dimension using the sine ratio.
- Solve for a missing dimension using the cosine ratio.
- Solve for a missing dimension using the tangent ratio.
- Solve for a missing angle using a trigonometric ratio.
- Describe less common trigonometric ratios.
- Solve for a missing dimension using a less common trigonometric ratio.
- Describe common methods for specifying tapers in prints.
- Calculate the taper per foot of a conical taper.
- Solve for the total included angle of a conical taper.

## Job Roles

## Certifications

NIMS- CNC Lathe Operations
- CNC Milling Operations
- CNC Milling Programming, Setup, & Operation
- CNC Milling: Programming, Setup, and Operations-FastTrack
- CNC Turning Programming, Setup, & Operation
- CNC Turning: Programming, Setup, and Operations-FastTrack
- Grinding I
- Grinding Skills-FastTrack
- Job Planning, Benchwork, & Layout I
- Job Planning, Benchwork, and Layout-FastTrack
- Measurement, Materials, & Safety I
- Measurement, Materials, and Safety-FastTrack

## Glossary

Vocabulary Term | Definition |
---|---|

acute angle | An angle that measures more than 0 degrees and less than 90 degrees. A reference angle is an acute angle in a right triangle. |

adjacent side | The side next to the reference angle in a right triangle. The adjacent side is not the hypotenuse. |

cosecant | CSC. A trigonometric ratio equal to the hypotenuse over the length of the opposite side. The cosecant ratio is the reverse of the sine ratio. |

cosine | COS. The ratio of the length of the adjacent side to the hypotenuse of the triangle. A cosine is a trigonometric function. |

cosine | COS. The ratio of the length of the adjacent side to the hypotenuse of the triangle. A cosine is a trigonometric ratio. |

cotangent | COT. A trigonometric ratio equal to the adjacent side over the length of the opposite side. The cotangent ratio is the reverse of the tangent ratio. |

cylindrical | A three-dimensional shape that has a circular base and top connected by walls. Cylindrical parts may have parallel or tapered walls. |

hypotenuse | The longest side of a right triangle. The hypotenuse is always opposite the 90 degree angle. |

included angle | For a taper, this is the entire angle that contains the taper. The legs of the included angle are formed by each edge of the taper. |

included angle | The entire angle that contains the taper. Each edge of the taper forms a leg of the angle. |

interior angles | The angles located within a closed figure. A triangle has three interior angles. |

inverse operation | An operation that counteracts or undoes another. The inverse tangent is used to find missing angles. |

opposite side | The side across from the reference angle in a right triangle. Knowing the measurement of the opposite side helps when solving for other missing dimensions. |

part drawing | A document that includes the specifications for a part's production. Using a right triangle in a part drawing can help to solve for unknown dimensions. |

reference angle | A known angle used to label the sides of a right triangle. The reference angle cannot be the triangle's right angle. |

right angle | An angle formed by two lines that are perpendicular to one another and measures exactly 90 degrees. A right triangle is characterized by its single right angle. |

right triangle | A triangle containing exactly one 90° angle. The other two angles must total exactly 90 degrees. |

rounding | A method used to shorten numbers. Rounding involves either increasing or decreasing a number to the next digit. |

secant | SEC. A trigonometric ratio equal to the length of the hypotenuse over the length of the adjacent side. The secant ratio is the reverse of the cosine ratio. |

sine | SIN. The ratio of the length of the opposite side to the length of the hypotenuse of a right triangle. Sine is a trigonometric function. |

sine | SIN. The ratio of the length of the opposite side to the length of the hypotenuse of the triangle. A sine is a trigonometric function. |

SOHCAHTOA | An acronym used to remember trigonometric ratios. Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent. |

symmetrical | A quality in which all the features on either side of a point, line, plane, or blueprint are identical. Both sides of a symmetrical part have the same dimensions. |

symmetrical | A shape that is able to be divided into two equal halves, with identical features in both halves. Symmetrical objects have sides that appear as mirror images of each other. |

tangent | TAN. The ratio of the length of the opposite side to the length of the adjacent side. A tangent is a trigonometric function. |

taper | A gradual decrease in diameter from one end of an object to another. Taper dimensions can be found using trigonometry. |

taper per foot | TPF. The difference in the size of a part from large to small diameter. Taper per foot is usually expressed as a ratio and is calculated in inches per foot. |

trigonometric ratios | A ratio that describes a relationship between a side and an angle of a right triangle. Trigonometric ratios include sine, cosine, and tangent. |