Trigonometry is a branch of mathematics that studies the trigonometric functions of angles( sine, cosine, tangent, cotangent, secant, cosecant) and the relationship between them. One of its applications are surveying and navigation. The methods in trigonometry are used to solve the relations in triangles.
Glossary
- Triangle: Polygon with 3 sides and 3 angles
- Right Angle: Angle that measures 90 degrees or one half of a pi radian
- Right Triangle: A triangle with one right angle
- Hypotenuse: The side of a triangle that is directly opposite of the right angle
- Pythagorean Theorem: States that the square of the hypotenuse is equal to the sum of the squares of the other two sides in a right triangle
- Trigonometric Functions: Sine, Cosine, Tangent, Cotangent, Secant, Cosecant
- Trigonometric equations: Equations that involve trigonometric functions; they often require calculating angles
- Trigonometric representation of a complex number Any complex number z can be written as z=r(cos(t)+i sin(t)), where r is a positive number called magnitude(modulus) and t is the argument, an angle in the range 0 to 2π. Geometrically, the magnitude is the distance from z to the origin while the argument is the angle between z and origin in counterclockwise direction.
- Trigonometric identity: An equation between two trigonometric expressions which is satisfied by any angle
- Trigonometric curve: The graph of the a trigonometric function in rectangular coordinates
- Trigonometric expression: An expression that includes at least one trigonometric functions.
Trigonometric series
Unit circle
Using the symmetries of the unit circle, you can memorize the values of the trigonometric functions at specific angles. The cosine value is given by the x-coordinate of a point on the unit circle, while the sine value is given by the y-coordinate. For example, when the angle is π/3 or 45 degrees, its corresponding point in the circle is (1/2,√3/2). This shows that cos(π/3)=1/2 and sin(π/3)=√3/2 .
A trick to remember the Unit Circle
A way to remember the Entire Unit Circle
Uses of Trigonometry
Wikipedia: Uses of Trigonometry
Math Careers: What's the Use of Trigonometry?
Algebra for the Athletes.com: Land Surveyors & Trigonometry
U.S. Department of Energy: Careers & Trigonometry
References
Fast Facts
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Fact:
Was probably invented for nautical navigation
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Fact:
Origins can be traced to ancient Egypt
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Fact:
First recorded use came from Hipparchus
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Fact:
Ptolemy further developed trigonometric calculations
