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## Class Details

- Class Name:
- Trig: Sine, Cosine, and Tangent 215
- Description:
- This class explains how to use sine, cosine, and tangent to find information about the sides and angles of right triangles in sample shop prints.
- Version:
- 1.0
- Difficulty:
- Intermediate
- Number of Lessons:
- 17
- Additional Language:
- Spanish, Chinese
- Related 2.0 Class:
- Trigonometry: Sine, Cosine, Tangent 211

## Class Outline

- Objectives
- Right Triangle Relationships
- Labeling Right Triangles
- Sine, Cosine, and Tangent
- SOHCAHTOA
- Sine: Finding a Missing Dimension
- Cosine: Finding a Missing Dimension
- Tangent: Finding a Missing Dimension
- Finding a Missing Angle
- Cosecant, Secant, and Cotangent
- Calculating Tapers
- Taper per Foot: Sample Problem
- Taper per Foot: Solution
- Finding a Taper Angle: Sample Problem
- Finding a Taper Angle: Sample Problem #2
- Sample Problem #2: Solution
- Summary

## Objectives

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

## Job Roles

- Assembly Mechanic
- Master Mechanic
- Autoclave Technician
- Automated Fiber Placement / Automated Tape Layup
- Composite Fundamentals
- Composite Repair Technician
- Composites Cutter and Kitting
- Filament Winding Operator
- Hot Press / Compression Mold Operator
- Infusion Operator
- Manual Layup Technician
- Manual Sprayup Technician
- Pultrusion Operator
- Trim, Drill and Finishing Technician
- Die Maker
- Electron Beam Welding Operator
- Fundamentals
- Hydroforming Operator
- Laser Cutter Operator
- Laser Welding Operator
- Lead Press Operator/Setup
- Press Brake Operator
- Roll Forming Operator
- Stamping Press Operator
- Tube/Bar Bending Operator
- Waterjet Operator
- CNC Programmer
- Grinding Technician
- Lathe Operator
- Machining Fundamentals
- Mill Operator
- Production Grinder
- Production Machinist
- Quality Technician
- Toolmaker / Diemaker
- Waterjet Operator
- Wire EDM Operator
- Automation (Motion Control, Robotics) Technician
- Electrical Maintenance Technician
- Fluid Systems Technician
- Mechanical Maintenance Technician
- Blow Mold Material Handler
- Blow Mold Operator
- Blow Mold Setup Person
- Blow Mold Technician
- Compression Mold Material Handler
- Compression Mold Operator
- Compression Mold Setup Person
- Compression Mold Technician
- Extrusion Material Handler
- Extrusion Operator
- Extrusion Setup Person
- Extrusion Technician
- Fundamentals
- Injection Mold Material Handler
- Injection Mold Operator
- Injection Mold Setup Person
- Mold Maker

## Certifications

SME- CMfgT

- CNC Lathe Operations
- CNC Milling Operations
- Job Planning, Benchwork, & Layout I
- Turning Operations: Turning Between Centers
- Turning Operations: Turning Chucking Skills

- MSSC Quality Practices and Measurement

## Glossary

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

adjacent side | The side next to the reference angle in a right triangle. The adjacent side cannot be the hypotenuse. |

CAH | Cosine is adjacent over hypotenuse. |

cosecant | In a right triangle, the ratio of the length of the hypotenuse divided by the opposite side of the angle. Cosecant is the reverse of sine. |

cosine | In a right triangle, the ratio of the length of the side adjacent to the angle divided by the hypotenuse. |

cotangent | In a right triangle, the ratio of the length of the adjacent side divided by the length of the opposite side of the angle. Cotangent is the reverse of tangent. |

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

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

minute | A unit of measurement used to describe angles. There are 60 minutes in 1 degree. |

opposite side | The side across from the reference angle in a right triangle. |

reference angle | The measured, or known angle in a right triangle other than the 90° angle. |

right triangle | A triangle containing one angle that measures exactly 90 degrees. |

secant | In a right triangle, the ratio of the length of the hypotenuse divided by the adjacent side of the angle. Secant is the reverse of cosine. |

second | A unit of measurement used to describe angles. There are 60 seconds in 1 minute and 60 minutes in 1 degree. |

sine | In a right triangle, the ratio of the length of the side opposite the angle divided by the hypotenuse. |

SOH | Sine is opposite over hypotenuse. |

SOHCAHTOA | A common phrase that helps visualize the relationship between the trigonometric ratios. Each letter represents the ratios in order. |

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

tangent | In a right triangle, the ratio of the length of the side opposite the angle divided by the length of the adjacent side. |

taper | A conical object with a gradual decrease in diameter from one end to another. On a shop print, a taper forms a right triangle. |

taper per foot | A measurement unit for a taper indicating the change in diameter for each foot along the taper's length. |

TOA | Tangent is opposite over adjacent. |

trigonometric ratio | A ratio that describes a relationship between the sides and angles of a triangle. |