Welcome to Trigonometry! We’ll be “Getting’ Triggy” with these concepts… 6.1: find exact values of trigonometric functions (5-1) 6.2: find coterminal and reference angles and to covert between units of angle measure (5-1) 6.3: solve for missing values in right triangles (5-4, 5-5) 6.4: use the law of sines and cosines and corresponding area formulas (5-6) 6.5: use the ambiguous case of the law of sines to solve problems (5-7)

In this section we will answer… 6.1 find coterminal and reference angles and to convert between units of angle measure (5-1) In this section we will answer… How are angles measured in Trig? What are the different units of angle measure within degree measurement? What does it mean for angles to be co-terminal? How can I find a reference angle?

Angles and Their Measures From Geometry:

In Trig Angles are always placed on the coordinate plane. The vertex is at the origin and one side (the initial side) lies along the positive x-axis. The other side (the terminal side) lies in a quadrant or on another axii. This is called Standard Position.

Angle Direction: Angles can be measured in two directions. Counter-clockwise is positive. Clockwise is negative.

Degree Measurement: One full rotation = _________________. The circle has been cut into 360 equal pieces. Measure of less than a degree can be shown 2 ways: Decimal pieces: 55.75º Minutes and seconds: used for maps 103º 45’ 5” Each degree is divided into 60 minutes. Each minute is divided into 60 seconds. 1º = 60’ = 3600”

Example 1 Change to minutes and seconds

Example 1 Change to minutes and seconds

Example 3 Change to decimal form

Example 4 Change to decimal form

Translating Rotations to Degrees Give the angle measure which is represented by each rotation: Example 1 5.5 rotations clockwise Example 2 3.3 rotations counterclockwise

Coterminal Angles Angles in standard position which share the same terminal side. 150º - 210º

Finding Coterminal Angles Simply add or subtract 360º as many times as you like. To write a statement to find EVERY angle coterminal with a certain angle:

Identify all the angles which are coterminal with the given angle Identify all the angles which are coterminal with the given angle. Then find one positive and one negative coterminal angle. Example 1 86º Example 2 594º

If each angle is in standard position, a) State the quadrant in which the terminal side lies b) Determine a coterminal angle that is between 0º and 360º. Example 1 595º Example 2 -777º

Reference Angle: The acute angle formed by the terminal side of an angle in standard position and the x-axis. The quickest route to the x-axis. Let’s find some!

Homework: P280 #19 – 65 odd