Chapter 7: Trigonometric Functions Section 7.1: Measurement of Angles.

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1 Chapter 7: Trigonometric Functions Section 7.1: Measurement of Angles

2 Recall: An angle is formed by two rays sharing a common endpoint. The initial ray is where the angle measure begins. The terminal ray is where the angle measure ends.

3 Types of Angles Positive angle – counterclockwise rotation from the initial ray. Negative angle – clockwise rotation from the initial ray.

4 Common Angle Measures Fill in as many angle measures as you recall from Geometry: Acute: Obtuse: Right: Straight: Reflex:

5 Reflex Angles A Reflex Angle is one which is more than 180° but less than 360°

6 Units of Angle Measure Degree – common unit for smaller angles. Revolution – common unit for larger angles. Radian – the number of radius units in the arc length of the angle.

7 Conversions Degrees to radians use: Degrees ∙ Radians to degrees use: Radians ∙

8 Example 1: Covert the following degree measures into radian measures: 1)96º 2)27º 3)21º 4) 49º

9 Example 2: Convert the following radian measures to degree measures: 1)7π 2) 3)2π 4)

10 Central Angle To find the measure of a central angle, θ, use the following formula: θ = where s is the arc length and r is the radius of the circle.

11 Example 7: Using the formula, find the measure of the central angle, θ, if the radius is 8 and the arc length is 6.

12 HOMEWORK (Day 1) pg. 261; 2 – 10 even (parts a and b only)

13 Standard Position An angle is in standard position when it is shown on the coordinate plane with its vertex at the origin and the initial ray along the positive x-axis.

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15 Other Special Angles Quadrantal angle – an angle where the terminal ray in standard position lies along an axis. The quadrantal angles are 0°, 90°, 180°, 270°, 360°, 450°, etc. and – 90°, – 180°, – 270°, – 360°, etc.

16 Coterminal angles – two angles (angles with the initial side on the positive x-axis) that have the same terminal ray when they are in standard position.

17 Coterminal Angles To find a positive coterminal angle, add 360º or 2π. Ex. 3: Find a positive coterminal angle of 74º. 434° Ex.4: Find a positive coterminal angle of.

18 Coterminal Angles To find a negative coterminal angle, subtract 360º or 2π until a negative angle is found. Ex. 5: Find a negative coterminal angle of 390º. -330° Ex. 6: Find a negative coterminal angle of π. - π

19 HOMEWORK (Day 2) pg. 262; 18 – 20 all