Trigonometry

Study of triangles and trigonometric functions including sine, cosine, and tangent.

Understanding Angles and TrianglesSine, Cosine, and Tangent FunctionsThe Unit Circle and Radian Measure
Trigonometric Identities and FormulasSolving TrianglesGraphs of Trigonometric Functions
Measuring Heights and DistancesTrigonometry in Engineering and DesignNavigation and GPS
Memorizing Trigonometric ValuesSolving Word Problems with DiagramsChecking Your Work with Inverse Functions
Understanding Angles...Sine, Cosine, and Ta...The Unit Circle and ...Trigonometric Identi...Solving TrianglesGraphs of Trigonomet...Measuring Heights an...Trigonometry in Engi...Navigation and GPSMemorizing Trigonome...Solving Word Problem...Checking Your Work w...
Basic Concepts

Understanding Angles and Triangles

What are Angles and Triangles?

Angles are formed when two rays meet at a common point. In trigonometry, we often measure angles in degrees (\(^{\circ}\)) or radians (\(\pi\) units). Triangles are shapes with three sides and three angles, and they're the stars of trigonometry!

Types of Triangles

  • Right Triangle: Has one angle of exactly \(90^{\circ}\).
  • Acute Triangle: All angles are less than \(90^{\circ}\).
  • Obtuse Triangle: One angle is more than \(90^{\circ}\).

Naming the Parts

In a right triangle:

  • The hypotenuse is the longest side, opposite the right angle.
  • The other two sides are called legs.

By understanding these basics, you'll be ready to dive into trigonometric functions!

Examples

  • A triangle with sides 3, 4, and 5 units forms a right triangle.

  • A triangle with angles 60°, 60°, and 60° is called equilateral.

In a Nutshell

Triangles and angles are the building blocks of trigonometry.

Key Terms

Hypotenuse
The longest side of a right triangle, opposite the right angle.
Right Angle
An angle that measures exactly 90 degrees.
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Sine, Cosine, and Tangent Functions