Trigonometry Chapter 1 1 1 Angles Basic Terminology

Trigonometry Chapter 1 1. 1 Angles

Basic Terminology Line Ray An Angle is formed by rotating a ray around its endpoint. negative angle positive angle

Basic Terminology The ray in its initial position is called the initial side Terminal side of the angle. Vertex A Initial side The ray in its location after the rotation is called the terminal side of the angle. The endpoint of the ray is the vertex of the angle.

Basic Terminology The most common unit for measuring angles is the degree. To use degree measure, we assign 360 degrees to a complete rotation of a ray. 1/360 of a complete rotation A complete rotation

Basic Terminology Acute angle: An angle measuring between 0 and 90 degrees. Right angle: An angle measuring exactly 90 degrees. Obtuse angle: An angle measuring more than 90 degrees but less than 180 degrees. Straight angle: An angle measuring exactly 180 degrees.

Basic Terminology Angles Acute Right Obtuse Straight We will use the Greek letter theta , along with many others to name each angle.

Basic Terminology Some Greek Letters: Lower case: Alpha: Pi: Beta: Lambda: Delta: Epsilon: Sigma: Rho: Upper case: Alpha: Pi: Beta: Lambda:

Basic Terminology Complementary Angles: two positive angles whose sum is 90 degrees. Supplementary Angles: two positive angles whose sum is 180 degrees. Example: Solve for m.

Basic Terminology Standard Position An angle is in standard position if its vertex is at the origin and its initial side is along the positive x-axis. y Q 1 Q 2 Q 1 Terminal side vertex x Initial side Q 3 Q 4

Basic Terminology Coterminal angles are angles that have the same terminal side. The measure of their angles differ by multiples of 360 degrees. To find coterminal angles just add or subtract multiples of 360 degrees. y y x Coterminal angles (positive) x Coterminal angles (negative)

Basic Terminology Examples: Find the angles of smallest possible positive measure coterminal with each angle. (a) (b)

Basic Terminology Sometimes it is necessary to find an expression that will generate all angles coterminal with a given angle. If we let n represent the multiple of 360 degrees then the expression that will generate all coterminal angles is: If n is 1, we are adding 360 degrees. If n is 2, we are adding 720 degrees. If n is -1, we are subtracting 360 degrees, etc.

Basic Terminology Questions? Homework: – Read section 1. 3 – Complete assignment 1. 1, due next class – Be prepared for daily points and vocabulary quizzes.