Finding the length of an intercepted arc - 3/7/13

•Topic: Periodic Functions and Trigonometry

•Aim: How can we find the length of an intercepted arc?

•Do Now: Write 90° in radians. Then identify the cos and sin of the angle

•Problem 3 on pg 838

•Finding the length of an arc

•Use the formula s = rθ, where s = length of the arc, r = radius and θ = angle measure in radians

•Example: if r = 3” and θ = 5π/6 radians, then s (the length of the arc) = (3)(5π/6) = 5π/2. We now simplify to get estimated inches using calculator ≈ 7.9. Therefore the arc has a length of about 7.9”

•Complete on your own

•Got it? #3 a and b on handout

•Then complete # 21 – 26 on back (Practice 13-3)

•All problems on this sheet #1 – 26 will be collected today and count as 50% of an assessment; the other 50% will be an in class quiz on Monday!

•Exit slip

•How many radians are in  60°?•

•How many degrees are in 5π/6 radians?

•Sketch these angles in the unit circle and label their x and y coordinates.

•Finding cosine and sine of a radian measure

•Vocabulary

•Central Angle: an angle of a circle with vertex at the center.

•Intercepted arc: portion of the circle with endpoints on the sides of the central angle and remaining points within the interior of the angle

•Radian: measure of a central angle that intercepts an arc with length equal to the radius of the circle.