MATHPOWER TM 12, WESTERN EDITION Chapter 4 Trigonometric Functions 4.1

4.1.2 An angle is formed by rotating an initial arm about a fixed point. Angles in Standard Position - Definitions An angle is said to be in when the is on the and the is at Positive angles have a rotation. Negative angles have a rotation. A is the angle measured from the to the terminal arm. The principal angle is A is the angle measured from the to the terminal arm. The reference angle is are angles that share the

4.1.3 Sketching Angles in Standard Position Sketch the following angles in standard position. State the principal angle, the reference angle, and one positive and one negative coterminal angle. a) b) c) Principal Angle Reference Angle Coterminal Angles Principal Angle Reference Angle Coterminal Angles Principal Angle Reference Angle Coterminal Angles

d) Principal Angle Reference Angle Coterminal Angles  where n is an element of the integers. Sketching Angles in Standard Position To find all coterminal angles: 4.1.4

Radian Measure A is the measure of the angle at the centre of the circle subtended by an arc equal in length to the radius of the circle. r r r 2r2r r r number of radians =

r Changing Degree Measure to Radian Measure Therefore,

4.1.7 Changing Degree Measure to Radian Measure Calculate the radian measure: a) b) 315 0

4.1.8 Changing Radian Measure to Degree Measure Calculate the degree measure: a) b) c) 1.68 rad To convert from radians to degrees, multiply by To convert from degrees to radians, multiply by

4.1.9 Finding the Sector Angle or the Arc Length Find the measure of the sector angle: 6.1 cm 5 cm Find the arc length: 8 cm 70 0 Convert 70 0 to radians: The arc length is cm. a

Angular Velocity Radians are often involved in applications involving angular speed. Angular speed is the rate at which the central angle is changing. Find the average angular speed of a wheel that is rotating 15 times in 3 s. Each time that the wheel rotates, it turns through a central angle of radians. Therefore, in rotations, the wheel has travelled radians. speed = The average angular speed is speed =

Suggested Questions: Pages , 2, 3-71 odd, 74, 80, 81,