Section 4.1A Trigonometry (Degrees and Radians) - Measurement of triangles

Rotation and Degree Measure Terms: Angle - determined by rotation of a ray about its endpoint

Initial side - starting position of the ray Terminal side - position after rotation of the ray

Positive angles - generated by counter-clockwise rotation Vertex - endpoint of the rays

Negative angles - generated by clockwise rotation

Ex 1: Find the degree measure of an angle represented by 2 Ex 1: Find the degree measure of an angle represented by 2.1 rotations counter-clockwise. 756º Ex 2: Find the degree measure of an angle represented by 1.5 rotations clockwise. -540º Ex 3: Find the number of rotations for a degree of measure 1512º. 4.2 rotations counter-clockwise

Radian Measure A central angle is an angle whose vertex is the center of a circle. One radian is the measure of a central angle that intercepts at arc whose length is equal to the length of the radius of the circle. 1 revolution = 360° = 2π radians 180° = π radians

Conversion between degrees and radians Since 360° = 2π radians and 180° = π radians the conversion that we use to convert from degrees to radians is: Also, the conversion that we use to convert from radians to degrees is:

Ex 4: Convert the following degree measures to radians (give answers in exact form). a. 135º b. 540º c. -270º d. 400º

Ex 5: Convert the following radian measures to degrees (round to the nearest 10th if necessary). a. b. 2 c. d.

II I III IV Quadrants are labeled with Roman numerals counter-clockwise from the top right. II I III IV

Suggested Assignment: Section 4.1A pg 255 – 256 #5 – 8, 27 – 30, 45 – 64