C H. 4 – T RIGONOMETRIC F UNCTIONS 4.1 – Radian and Degree Measure

A NGLES Every angle has an initial side and a terminal side Counterclockwise  positive angle measure Clockwise  negative angle measure Coterminal angles have the same terminal sides and are coterminal Vertex Terminal side Initial side An angle in standard form: Initial side Terminal side

R ADIANS We know 2 ways to measure angles: degrees and radians Radian = measure of a central angle, θ, that intercepts an arc, s, that is equal to the radius, r, of the circle In general, s = rθ is the formula for arc length The total radians in one revolution is 2π By adding multiples of 2π, one can find coterminal angles Complementary angles add to 90 °; supplementary angles add to 180°

R ADIANS Ex: Convert 225° to radians. Set up a proportion! We know 360° is 2π radians, so… Ex: Convert (7π/12) to degrees.

C ONVERT FROM RADIANS TO DEGREES ° 2. 90° ° 4. 45° °

C ONVERT 38 ° FROM DEGREES TO RADIANS

F IND THE COMPLEMENT OF

F IND AN ANGLE COTERMINAL WITH

A DDITIONAL ANGLE TOPICS Sometimes angles will be given in D ° M’ S’’ form. D = degree M = minute; 60 min = 1° S = second; 3600s = 1° Ex: Convert 22° 24’ 45” to decimal degrees.

A DDITIONAL ANGLE TOPICS Linear speed along an arc = arc length per time unit Angular speed inside a circle = radians per time unit Ex: A bicycle wheel of radius 13 in. makes 8 revolutions per second. Find the angular speed of the wheel and the linear speed of the tire tread. Use dimensional analysis! Angular speed: Start with rev/s, end with rad/s Linear speed: Start with rev/s, end with in/s