Shop Essentials (Applied Mathematics)

#### Trigonometry: Sine, Cosine, Tangent 211

The class Trigonometry: Sine, Cosine, and Tangent discusses the three basic ratios that are the basis for trigonometry. Trigonometry is based on the specific relationships between the sides and angles of right triangles. Using trigonometry, a person can determine the missing angle and side measurements of a right triangle based on the information present in a drawing. Although solving trigonometric ratios often requires a calculator, users must know which ratios to apply to a particular problem and how to calculate them. In situations where parts are being manufactured, this knowledge is crucial to effective production of parts that require specific dimensions and angles.

After taking this class, a user should be able to define the various trigonometric ratios, and use them to solve various problems, including calculating a taper angle on a print.

• Difficulty Intermediate

• Format Online

• Number of Lessons 18

• Language English

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Course 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
• Tangent: Finding a Missing Dimension
• Trigonometry Calculator
• 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.
• Solve for the total included angle of a conical taper.
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.

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.

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.

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.

SOHCAHTOA

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

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.

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.

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.

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.

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.