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Chapter 7: Trigonometric Functions Section 7.1: Measurement of Angles
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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.
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Types of Angles Positive angle – counterclockwise rotation from the initial ray. Negative angle – clockwise rotation from the initial ray.
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Common Angle Measures Fill in as many angle measures as you recall from Geometry: Acute: Obtuse: Right: Straight: Reflex:
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Reflex Angles A Reflex Angle is one which is more than 180° but less than 360°
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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.
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Conversions Degrees to radians use: Degrees ∙ Radians to degrees use: Radians ∙
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Example 1: Covert the following degree measures into radian measures: 1)96º 2)27º 3)21º 4) 49º
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Example 2: Convert the following radian measures to degree measures: 1)7π 2) 3)2π 4)
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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.
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Example 7: Using the formula, find the measure of the central angle, θ, if the radius is 8 and the arc length is 6.
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HOMEWORK (Day 1) pg. 261; 2 – 10 even (parts a and b only)
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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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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.
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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.
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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.
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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
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HOMEWORK (Day 2) pg. 262; 18 – 20 all
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