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Radian Measure and applications

Radian Measure and applications. Chapter 2 Circular Functions and Trigonometry. Measuring Angles. Why do we measure angles using degrees? Why are there 360 of them in a circle? What if I wanted to divide them into different pieces?. A radian An Intro. Look at this diagram- applet:.

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Radian Measure and applications

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  1. Radian Measure and applications Chapter 2 Circular Functions and Trigonometry

  2. Measuring Angles • Why do we measure angles using degrees? • Why are there 360 of them in a circle? • What if I wanted to divide them into different pieces?

  3. A radian An Intro • Look at this diagram- applet:

  4. What is a radian? • The measure of the CENTRAL angle subtended by an arc EQUAL IN LENGTH to the radius of a circle. • Here is a radian. • (the green angle) • There are 2π radians in a circle(find out why later!) • Click HERE to see how you get a radian.. There are also some questions to test you/

  5. 1 Radian

  6. A radian • Definition: if the circumference of a circle is 2пr how many r’s will go around the circle?

  7. The relationship • Yes 2  is equal to one full turn of a circle • So 2  = 360 0 • Or it is easier to remember •  = 180 0

  8. Complete this table

  9. Common angles • Click here to see some common angles in radians

  10. Arc length • How do we find the arc length? • Length of an arc l = θ X circumference 2п • Since the circumference is 2пr • Then: • So: l = rθ • Remember the angle θ is in radians!

  11. Area of a sector • Area of sector A = θX Area of a circle 2п • Since the area of a circle is пr2 • Then: • So: A = ½ r 2θ • Please Remember to use RADIANS

  12. Arc length, area of a sector • Area of a sector proof: • Arc length: • Please remember these angles in these two formulae are all in RADIANS!

  13. Radian • Click here for a game • Match the angles in degrees with radians here • Radian practice with trig functions here

  14. Area of a segment • Remember another formula or remember the method using common sense? • Let’s use our common sense! • What steps would you have to take to find the area of the segment?

  15. Finding the Area of a Segment Please use Radians! Find the area of the sector using A = ½ r 2θ Find the area of the triangle using ½ absinC What is the area of the segment? Segment = Sector –Triangle

  16. How to find the segment? • Calculate the area of the segment in the following diagram. The radius is 10cm and the central angle is /3c • Calculate the area of the sector • Calculate the area of the triangle • Calculate thee area of the segment

  17. How do I find the area of a segment? • Look at the following diagram and follow the hint steps to find the area of the segment. • Shade in the segment in the circle below. Label the triangle AOB. Angle AOB = 0.5 radians and the radius is 12 cm. • Find the area of the sector • Find the area of the triangle using ½ absinC • What is the area of the segment?

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