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Trig: Sine, Cosine, and Tangent 215

Shop Essentials Training

Class Information

Tooling U classes are offered at the beginner, intermediate, and advanced levels. The typical class consists of 12 to 25 lessons and typically requires at least two hours of instruction time.

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.
Prerequisites:	800205
Difficulty:	Intermediate
Number of Lessons:	17

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
What Is a Taper?
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
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.