## Shop Essentials (Applied Mathematics) Training

Class Information
 Tooling U-SME classes are offered at the beginner, intermediate, and advanced levels. The typical class consists of 12 to 25 lessons and will take approximately one hour to complete.
 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. Difficulty: Intermediate Number of Lessons: 17 Language: English, Spanish, Chinese

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

Class 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.

Class Vocabulary

Vocabulary TermDefinition
The side next to the reference angle in a right triangle. The adjacent side cannot be the hypotenuse.
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.
In a right triangle, the ratio of the length of the side adjacent to the angle divided by the hypotenuse.
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.
The longest side of a right triangle. The hypotenuse is always opposite the 90° angle in a right triangle.
The entire angle that contains the taper. Each edge of the taper forms a leg of the angle.
A unit of measurement used to describe angles. There are 60 minutes in 1 degree.
The side across from the reference angle in a right triangle.
The measured, or known angle in a right triangle other than the 90° angle.
A triangle containing one angle that measures exactly 90 degrees.
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.
A unit of measurement used to describe angles. There are 60 seconds in 1 minute and 60 minutes in 1 degree.
In a right triangle, the ratio of the length of the side opposite the angle divided by the hypotenuse.
Sine is opposite over hypotenuse.
A common phrase that helps visualize the relationship between the trigonometric ratios. Each letter represents the ratios in order.
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.
In a right triangle, the ratio of the length of the side opposite the angle divided by the length of the adjacent side.
A conical object with a gradual decrease in diameter from one end to another. On a shop print, a taper forms a right triangle.
A measurement unit for a taper indicating the change in diameter for each foot along the taper's length.