Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Unit 5: Trigonometry I (Day 1) Radian Measure Consider a circle of radius 1 (called a unit circle). i) How long is the arc contained by an angle of 90o? ii) 180o? iii) How many degrees is the angle containing an arc of length 2.5? Definition: 1 radian is the measure of an angle containing an arc of length r in a circle of radius r. To convert between degrees and radians: 180 o Similarly, 2 360 o Degrees Radians: Multiply by Radians Degrees: Multiply by 180 o 180 o Examples: Convert from degrees to radians: i) 30o ii) 90o iii) 45o iv) 110o v) 360o v) 270o * We often leave radians in terms of ** The units for radians are either: ‘radians’ or nothing. If an angle measures 2 , no units included, then we are working in radians. Convert from radians to degrees. i) 1 radian iii) ii) 5.6 radians 5 6 iv) 3 4 Finding the length of an arc in a circle of radius r: 1. Determine the fraction of the circle being worked with. 2. Multiply this by the circumference Degrees: Arc length = a Radians: Arc length = a 360o 2r 2r 2 Examples: i) A circle has radius 8 cm. Calculate the length of the arc subtended by each angle: a) 2.3 radians b) 75o ii) A circle has radius 5 cm. Find the angle at the center containing an arc length of: a) 6 cm (in degrees) b) 15 cm (in radians) ex: A bicycle wheel has a radius of 30 cm. What is the distance rolled if the wheel has turned: 45o 120o 1000o Homework: p. 485 #1-4 p. 494 #5, 8, 9