Civil

Civil engineers use trigonometry to measure and create designs of projects.

It can be used to calculate angles and distances in the designs of buildings, bridges and structures.

Sinusoidal functions can also be used to calculate structural properties such as beam deflection and structural integrity.

**Trigonometry in Engineering**

**By Garrett Murphy, Garrett Mazziotti, and Matthew Blewett**

Overview

Trigonometry is heavily used in many fields of study, such as science and engineering.

In the field of engineering, trigonometry is used in many different forms and is utilized in many different ways.

How Trigonometry is used in Engineering

Engineering is broken down into four main categories. They are....

Mechanical

Civil

Electrical

Chemical

Engineering

Electrical Engineering

A sinusoidal Function can be used to predict the direction and direction of an alternating Current

Civil Continued: Architecture

Trigonometry is used in architecture because it allows the architect to calculate different elements of a design such as distances and forces related to diagonal elements such as roofs and custom ceilings.

Of the six functions in basic trigonometry, the sine, cosine, and tangent are used to easily find the opposite and adjacent values related to an angle or hypotenuse.

Mechanical Engineering is one of the broadest engineering fields.

Mechanical engineers design, develop, build, and test mechanical and thermal devices, including tools, engines, and machines.

Mechanical engineers have to research, design, develop, manufacture, and test tools, engines, machines, and other mechanical devices.

This process is known as the "Design Process".

For the Mechanical engineers to be able to complete the design process they have to apply principles from calculus and trigonometry as well as other higher-level mathematics concepts.

The graph represents a normal sine function that starts at y=0

The max voltage of the current is 311 Volts, and so the minimum must reflect across y=0 and be -311 Volts

A therefor equals 311

There are no shifts present in the graph of the function.

So the function of the current must be y=311sin(1/3x)

Trigonometry

Trigonometry is the study of the relationships between the sides and angles of triangles.

Real world applications are seen in many different fields today , but particularly are in the many aspects of Engineering

The period of the function is 20ms.

So, (2 x pi)/B =20

B is about 1/3

Chemical Engineering

Sinusoidal Functions make up the basis for spectroscopy, which identifies the makeup of a material/substance by identifying the light radiated by said compound/material.

**Spectroscopy**

Different elements reflect and radiated different wavelengths of light.

Elements can be identified by looking at what color light is emitted.

Hydrogen

Oxygen

Another example of Trigonometry in Mechanical Engineering is to find heights for centers of mass

Use Force Triangles to determine

the height of the center mass

Mechanical Vibrations

Mechanical vibration is defined as the measurement of a periodic process of oscillations with respect to an equilibrium point.

Or the motion of a body or system of connected bodies displaced from a position of equilibrium.

There are many different kinds of Mechanical Vibration.

Two are Free and Forced vibration

Mechanical Vibrations are very similar to Sound, or "pressure waves," and are calculated in the same way.

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Another way that Trigonometry is Mechanical Engineering is to find distances or angles in joints in products