3.2 Angle Measures in Degrees & Radians. Another way to measure angles is in radians. 360  = 2π rad.  180  = π rad. –To convert from degrees to radians:

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Presentation transcript:

3.2 Angle Measures in Degrees & Radians

Another way to measure angles is in radians. 360  = 2π rad.  180  = π rad. –To convert from degrees to radians: Multiply the number of degrees by –To convert from radians to degrees: Multiply the number of radians by (Hint: to remember which one, think about what you want to cancel – that one goes on the bottom!)

Ex 1) Express each angle measure in radians (in terms of π) a) 135  b) –150  Ex 2) Express each angle measure in degrees (nearest tenth) a) b) 5.1

Arc Length (s) Arc length of a circle of radius r determined by central angle θ (in radians) is: Ex 3) Find the arc length to the nearest tenth of a cm of a circle of radius 7 cm that is intercepted by a central angle of 85  85° (convert to rad.) r s  (s & r have same units)

Ex 4) A pendulum swings through an angle of rad. describing an arc of 0.4 m long. Determine the length of the pendulum to the nearest tenth. 0.4

sector of a circle to find its area, we make a proportion θ r

Ex 5) Determine the area (to the nearest tenth of a sq. meter) of the sector of a circle of radius 1.6 m intercepted by a central angle of 45°

Homework #302 Pg 130 #1–47 odd