What is a RADIAN?!?!.

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Presentation transcript:

What is a RADIAN?!?!

♪♪Twinkle Twinkle Little Star Circumference Equals 2πr♪♪ Length of an arc (Arc Length): s = rθ s = (πrθ)/180 1 Revolution (Circumference): s = 2πr A radian is a unit of an angle equal to the angle at the center of a circle whose arc is equal to the length of the radius. How many degrees is a radian??

Arc Length Example A circle/pizza/tire/any round object has a radius of 6 inches. Find the length of the arc intercepted by a central angle of 120∘.

Area of a Sector Example For a circle of radius 𝑟, the area 𝐴 of a sector with central angle 𝜃 is given by 𝐴 = (1/2)r2𝜃 where 𝜃 is measured in radians. Example A sprinkler sprays water over a distance of 30 ft while rotating through an angle of 150∘. What area of lawn receives water?

Converting Radians  Degrees To convert from radians to degrees, multiply the number of radians by 180°/π radians.

Examples Convert radians to degrees. Convert radians to degrees.

Converting Degrees  Radians To convert from degrees to radians, multiply the number of degrees by π radians/180°.

Examples Convert 90° to radians. Convert 120° to radians.