Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Pythagorean theorem wikipedia , lookup
Integer triangle wikipedia , lookup
Line (geometry) wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Multilateration wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Euclidean geometry wikipedia , lookup
Euler angles wikipedia , lookup
Chapter 7: Trigonometric Functions Section 7.1: Measurement of Angles 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. Types of Angles Positive angle – counterclockwise rotation from the initial ray. Negative angle – clockwise rotation from the initial ray. Common Angle Measures Fill in as many angle measures as you recall from Geometry: Acute: Obtuse: Right: Straight: Reflex: Reflex Angles A Reflex Angle is one which is more than 180° but less than 360° 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. Conversions Degrees to radians use: Degrees ∙ 180 Radians to degrees use: Radians ∙ 180 Example 1: Covert the following degree measures into radian measures: 1) 96º 2) 27º 3) 21º 4) 49º Example 2: Convert the following radian measures to degree measures: 1) 7π 2) 6 5 3) 2π 4) 4 3 Central Angle To find the measure of a central angle, θ, use the following formula: s θ= r where s is the arc length and r is the radius of the circle. Example 7: Using the formula, find the measure of the central angle, θ, if the radius is 8 and the arc length is 6. HOMEWORK (Day 1) pg. 261; 2 – 10 even (parts a and b only) 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. 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. 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. 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 10 3 4 3 . 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 HOMEWORK (Day 2) pg. 262; 18 – 20 all