# Some of the Many Uses of Trigonometry...

Many students hate trigonometry. But that's a real shame because it is certainly one of the most useful bits of mathematics that you will learn. Your computer, phone, tablet or other device is using trignometry right now, allowing you to read this.

Following are some of the many applications of trigonometry - I hope you find them interesting.

### 1. Core Trigonometry

- In the Trigonometric Functions chapter:
- The Right Angle and Applications (surveying, geography)
- Applications of Radian Measure (arc length, area of a sector, angular velocity)

- In the Trigonometric Graphs chapter:
- Applications of Trigonometric Graphs (simple harmonic motion, angular velocity, mechanics)
- Composite Trigonometric Graphs (electronics, physics)
- Lissajous Figures (seen on oscilloscopes)

- In the Additional Topics in
Trigonometry chapter:
- Expressing a sin θ ± b cos θ in the form R sin(θ ± α) (used in electronics)

### 2. Complex Numbers

- In the Complex Numbers chapter:
- Polar Form (used in electronics)
- Exponential Form (used in electronics)
- Products, Quotients, Powers and Roots (used in electronics)
- Impedance and Phase Angle (used in electronics)
- Reactance and Angular Velocity (used in electronics)
- AC Circuit Exercises (used in electronics)
- Parallel AC Circuits (used in electronics)

### 3. Differentiation

- In the Differentiation of Transcendental Functions chapter:
- Applications: Derivatives of Trigonometric Functions (power, mechanics, rates of change)
- Applications: derivatives of Logarithmic and Exponential Functions (avaitaion, sound, electronics, radius of curvature)

- In the Applications of Differentiation chapter:
- Tangents and Normals (mechanics, rotating bodies, engineering)
- Newton's Method (approximating values)
- Curvilinear Motion (mechanics, engineering)
- Related Rates (mechanics)
- Applied Maximum and Minimum Problems (economics, mechanics, engineering)
- Radius of Curvature (engineering)

### 5. Integration

- In the Applications of Integration chapter:
- In the Methods of Integration chapter:
- Integration: Basic Trigonometric Forms (electronics)
- Integration: Other trigonometric Forms (Root mean square value - electronics)
- Integration: Inverse Trigonometric Forms
- Integrations by Trigonometric Substitution (a neat trick that makes complicated integrals easier)

- A student project:
- Integration Mini-Project (a math mini-project created by a student)

### 6. Differential Equations

From the Differential Equations chapter:

Solutions of Differential Equations

Application: Series RL Circuit

Some student projects:

DEs Project 2 (a math mini-project created by a student)

DEs Project 3 (a math mini-project created by a student)

### 7. Fourier Series

- Fourier Series (whole chapter)

### 8. Laplace Transformation

### 9. Matrices

- Matrices
(electronics)

Multiplication of Matrices (robot arm)

### 10. Plane Analytical Geometry

### 11. Systems of Equations

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