L. G. - "I can apply the laws of logs to simplify and/or evaluate logarithmic expressions." Properties of Logs i) log, 1 = 0 ii) log a* = x iii) a 10%.* = X Proofs: Product Law Exponents: atxa = atty Logarithms: log. mm = log, m + log, " provided a, m, and n > 0 Proof:\fUnit 5: Trigonometric Functions Date: L1: Radian Measure L.G.: "I can use radian measurement to represent the size of an angle." What is a RADIAN? Definition of a Radian Radians are an alternative way to measure angles, other than using degrees. The number of radians contained in an angle is equal to the ratio: # of radians = the length of the arc subtendedby the angle or 0 = the length of the radius of the circle Note: a ratio is unit-less so a radian is a "unit-less" unit for measuring angles! Question: How many radians are in a circle? . We can work in general with a circle of radius r. This will prove that the results we obtain will work for any size circle. The length of the arc that is subtended by a 360 angle is actually the of the circle. This is found by the formula .: # of radians in a full circle= Therefore, radians = 360. Example 1: Convert from degrees to radians. a) 90 Rule for conversion between DEGREES ( RADIANS is: b) 270 180 = radians 10 = radians c) 1380 # of degrees x = # of radiansUnit 5: Trigonometric Functions Date: Rule for conversion between RADIANS ( DEGREES is: Example 2: Convert from radians to degrees. At radians = a)- 4 1 radian = # of radians x = # of degrees 2 c) 1.45 Example #3: The London Eye Ferris wheel has a diameter of 135 m and completes one revolutions every 30 minutes. a) Determine the angular velocity, @ , in radians per second. (w = 0/t where 0 = angular displacement (rad), and t = time (s)) b) How far has a rider travelled at 18 minutes into the ride