University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2014
Views:

350

Pages:

2
Author:

contravavif

Math III Notes: Intro to Trigonometry Name Trigonometry: The study of the relationships among the angles and sides of a right triangle. rigonometric Functions: sine (sin), cosine (cos), tangent (tan) sin hyp PP cosadj tan hyp opp Recall: 11 22x2 adj sin cose tan X 30 45 30° 2x x√3 x√2 x 2x 45° 60° 45 60° = 2x 2 2x = 2x2 2x On a coordinate plane, an angle may be generated by the rotation of two rays that share a fixed endpoint at the origin. Initial side: The ray of the angle that is fixed along the positive x-axis. Terminal side: The ray of the angle that can rotate about the center. tandard position refers to an angle whose initial side is along the positive x-axis and whose vertex is at the origin. Terminal Side Vertex Degree: The measure of an angle determined by the amount of rotation. Unit Circle: A circle of radius 1 unit whose center is at the origin of a coordinate system. = theta Initial side Radian: The measure of an angle in standard position whose rays intercept an arc of length 1 unit on the unit circle. (note: the length of the intercepted are is equal to the radius of the circle.) C=2nr. In a unit circle: r = 1 therefore C=2#(1) or 2 units An angle representing one complete revolution of the circle measures 2 radians or 360°. Converting from radians to degrees (-1,0) (0,1) The Intercepted are 1 unit 1(1,0) (0,-1) Converting from degrees to radians 2 radians 360° 2π 360° 2π 2π 180° 1 radian = 360° 2 radians 360° 2л 360 360 radians 1°= 180 Rewrite each degree measure in radians and each radian measure in degrees. 1.-3.180 3 Π -300° 2.18°. Π 180 3.140°- 13 180 4. 30 5.-250° T 180 radians 6.9180 IT 180 T 10 7ㅠ 78° -25 TT 18 1620 515 عام *Unit Grcle is reflexive! Ay X sino = (y's) cos(x's) tang (ㄨ) 4 * every 45° is The Unit Circle * every 30° is Positive: sin I Negative cos, tan (0,1) 90 2 2 3 √2, 2 22 120° B 135° 22 150° T Positive: Sin, cos, tan Negative: 13 ( 100° 45° 30 r dista From (o to a po (,) (-10) 180° (1) 360° 21 210 225 4. 330° 6 315° 240% 1300° ( ) 3 2270° 2 ( ) Positive: tan IIL Negative: Sin, cos (0-1) TV Positive: COS Negative: sin, tan 120 120 or ex-24 480 Coterminal Angles: Two angles in standard position have the same terminal side. Example: 45° and 405° -70° and 290° X+360 x+2π X-360 x-2π Find one angle with positive measure and one angle with negative measure coterminal with each angle. 5 5