1- Describe Angels

​The word trigonometry means “measurement of triangles.”


An angle is determined by rotating a ray (half-line) about its endpoint.

Standard Position: An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis.

positive angles --> Counterclockwise rotation

negative angles --> clockwise rotation

coterminal --> angles α and β have the same initial and terminal sides. Such angles are coterminal.

Radian Measure

Radian: An angle measurement based on the radius

ways of measuring angles

1- Degree Measure:

• ​Full circle = 360 degrees

• Right angle = 90 degrees

• Straight angle = 180 degrees

2- Radian Measure:

• ​Full circle = 2π radians

• Half circle = π radians

A radian is the angle where the arc length equals the radius length

Example 1: Finding Coterminal Angles

​Add or subtract 2π to get coterminal angles Formula: θ ± 2π

Solve: Determine two coterminal angles (one positive and one negative) for each angle.

a) θ = π/4

Degree Measure

​A second way to measure angles is in degrees, denoted by the symbol °.