Radian Measure and applications

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Presentation transcript:

Radian Measure and applications C2 Chapter 6

A radian An Intro Look at this diagram- applet:

1 Radian

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

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

Complete this table Radians Degrees 3/4 c /2 c 90 /4 c 3 /2 c 1 c 270 0 150 0 120 0 330 0

Common angles Click here

Arc length Do you want to see the proof or just the formula? Length of an arc l = θ Circumference 2п The proportions are the same! Since the circumference is 2пr Then l = rθ Remember the angle θ is in radians!

Area of a sector Area of sector A = θ area of circle 2п Since the area of a circle is пr2 A = ½ r 2 θ Please Remember to use RADIANS

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!

Arc length To find the arc length of a circle when the angle subtended is given in radians we use this formula: Arc length = r  where r is the radius and  is the angle subtended in radians r

Radian Click here for a game Match here Radian practice with trig functions here

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?

Finding the Area of a Segment Please use Radians!

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?