4-1 Review 1. Convert -4.2 radians to degrees

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Presentation transcript:

4-1 Review 1. Convert -4.2 radians to degrees 2. Order from smallest to largest: 1 revolution, 1 degree, 1 radian

4-1 Review 1. Convert -4.2 radians to degrees -4.2 rad x ( 180°/Π rad ) = -756°/ Π = -240° 2. Order from smallest to largest: 1 revolution, 1 degree, 1 radian 1 degree, 1 radian, 1 revolution

Quote of the Day “A good hockey player plays where the puck is. A great hockey player plays where the puck is going to be.” -Wayne Gretzky

4-2 Lengths of Arcs and Areas of Sectors Circumference of a circle=2∏r = ∏d Area of a circle= ∏r2 Example: Find the length of arc AB if A m<ACB = 75° and the radius B is 6 cm. C C = (75/360) x ∏ x 12 = (5/2) ∏

Arc Length in Radians Arc length in degrees = θ/360° ◦ 2∏r (θ=angle measure in degrees, r=radius) Converting this formula to radians… Because 360° = 2∏, 360 and 2∏ cancel in the formula. So, Arc length in radians = θr (θ = angle measure in radians, r=radius) *Use the 1st formula for degrees and the 2nd one for radians.

Example Find the length of an arc of a central angle with measure ∏/3 radians in a circle with radius 5 cm. Arc length in radians = θr = ∏/3 ◦ 5 = 5∏/3 cm

Area of a Sector A = θ/360° ◦ ∏r2 (in degrees) Convert to radians: Knowing that ∏ radians = 180°, use substitution A = θ/360° ◦ 180r2 = 180 θr2 / 360 Reduce and get (180 goes into 360 twice): Area of a sector in radians= θr2 / 2

Example of area of a sector Find the area of a sector of a circle with radius 10 cm and central angle 2∏/3 radians. A = θr2 / 2 = (2∏/3) ◦ 100 / 2 = (2∏/3) ◦ 50 = 100 ∏/3 or 104.7 sq. cm Exact approximate (Better answer)

How fast are we moving? Earth travels around the sun in an elliptical orbit, but one that is nearly circular with radius 93,000,000 miles. Using the circular approximation, about how far does the Earth travel in a single day? Use 365.25 days for the length of one year. 1/365.25 revs ◦ 2∏ / 1 rev = 2∏ / 365.25 rad. s = θr = 93,000,000 ◦ 2∏ / 365.25 = =1,599,825.4 miles How many miles per hour is that?

“Earth Rise”

Assignment Do pages 242-243 1-4, 11-14, 18-20