Lessons In Electric Circuits -- Volume V (Reference) - Chapter 5

Lessons In Electric Circuits -- Volume V

Chapter 5

TRIGONOMETRY REFERENCE

• Right triangle trigonometry
  • Trigonometric identities
  • The Pythagorean theorem
• Non-right triangle trigonometry
  • The Law of Sines (for any triangle)
  • The Law of Cosines (for any triangle)
• Trigonometric equivalencies
• Hyperbolic functions
• Contributors

Right triangle trigonometry

A right triangle is defined as having one angle precisely equal to 90^o (a right angle).

Trigonometric identities

H is the Hypotenuse, always being opposite the right angle. Relative to angle x, O is the Opposite and A is the Adjacent.

"Arc" functions such as "arcsin", "arccos", and "arctan" are the complements of normal trigonometric functions. These functions return an angle for a ratio input. For example, if the tangent of 45^o is equal to 1, then the "arctangent" (arctan) of 1 is 45^o. "Arc" functions are useful for finding angles in a right triangle if the side lengths are known.

The Pythagorean theorem

Non-right triangle trigonometry

The Law of Sines (for any triangle)

The Law of Cosines (for any triangle)

Trigonometric equivalencies

Hyperbolic functions

Note: all angles (x) must be expressed in units of radians for these hyperbolic functions. There are 2π radians in a circle (360^o).

Contributors

Contributors to this chapter are listed in chronological order of their contributions, from most recent to first. See Appendix 2 (Contributor List) for dates and contact information.

Harvey Lew (??? 2003): Corrected typographical error: "tangent" should have been "cotangent".

Lessons In Electric Circuits copyright (C) 2000-2006 Tony R. Kuphaldt, under the terms and conditions of the Design Science License.