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Understanding Trigonometric Identities and Circle Geometry Concepts

This lesson covers key trigonometric identities such as sine, cosine, tangent, secant, and cosecant, emphasizing their relationships. We will explore the fundamental components of a circle, including the diameter, radius, center, minor and major arcs, and semicircles. Students will learn how to measure central angles and their corresponding arc lengths. The investigation will highlight the important relationship where the sum of central angles in a circle equals 360 degrees. Important formulas for arc length and angle measures will be discussed.

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Understanding Trigonometric Identities and Circle Geometry Concepts

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  1. 26 April 2011 Precalculus

  2. Simplify: sinqcosqsecqcotq • sinq • cosq • tanq • secq • cscq 300 0 of 30

  3. Agenda • Last trig identity • Circle Intro • Parts of a Circle • Central Angle Measure • Arc Measure • Arc Length

  4. Circle Investigation Day 1 4/26 Parts of a Circle Diameter

  5. Circle Investigation Day 1 4/26 Parts of a Circle Radius

  6. Circle Investigation Day 1 4/26 Parts of a Circle Center

  7. Circle Investigation Day 1 4/26 Parts of a Circle Minor Arc

  8. Circle Investigation Day 1 4/26 Parts of a Circle Major Arc

  9. Circle Investigation Day 1 4/26 Parts of a Circle Semicircle

  10. Circle Investigation Day 1 4/26 Parts of a Circle Central Angle

  11. Circle Investigation Day 1 4/26 Parts of a Circle A central angle and its arc will always have the same measure.

  12. Circle Investigation Day 1 4/26 The central angles of a circle always sum to 360o. Central Angle Measure

  13. Circle Investigation Day 1 4/26 <AEB + <BEC + <CED + <DEA = 360o Central Angle Measure

  14. Circle Investigation Day 1 4/26 Sometimes you will be asked to find either arc length, or the central angle measure. Use the following proportion to solve: M = central angle measure L = arc length r = radius Arc Measure

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