University:
Missouri State University
Course:
MTH 136 | Precalculus 1
Academic year:

2020
Views:

41

Pages:

5
Author:

iwanankgfd

PRE-CALCULUS/TRIG 3 Name: Key Date: 4.2 Trig Functions & the Unit Circle SOH-CAH-TOA sin e theta= oppocsite hypolcnuse cos theta= OCl (Ocent hypotenuse opp hyp adj UNIT CIRCLE (radius of 1 mn mgemt = 0ppj * 0 site cdjocent Reciprocal Identities (CSC)/(sec(ant)) = hupotenite 9posite se * (Sec)/(sec(ant)) * o = huooteruse odjacent cotangent a = odiacent opposite Ref radius hyp 1 adj y opp 45 deg - 45 deg - 90 deg 1x - x + 12x Coordinates on unit circle: (x, y) → (Cose. Sine SPECIAL RIGHT TRIANGLES (USING THE UNIT CIRCLE) ny = sqrt 2 * log 1/(sqrt(2)) = (7x)/(sqrt(2)) 30 deg - 60 deg - 90 deg 1x - sqrt(3) * x - 2x 1 1 PP 2 1 sty 45 deg 30° 2013 60° 1 X X hyp=2-sl X cos 30 deg = (sqrt(3))/7/1 (x ^ 2)/2 ll = sqrt(3) * Delta*l ll = sqrt(3) * 1/2 x = (sqrt(3))/2 X hyp 1 = 2x -> x = 1/2 dd = sqrt(3) * Delta*l cos 60 deg = 1/2/((sqrt(3))/2) y = (sqrt(3))/2 Af = sqrt(3) * 1/2 y sin 45 deg = psi L 2\ 2\ y sin 30 deg = 1/2 cos theta = X/I = X tan theta = y/x = (sin varphi)/(cos theta) csc(theta) = 1/y = 1/(sin theta) sec(theta) = 1/X = 1/(cos theta) sin theta = y/1 = y cot theta = x/y = (cos theta)/(sin theta) = 1/(tan theta) x = 1/(sqrt(2)) * (sqrt(2))/(sqrt(7)) x = (sqrt(2))/2 cos 45 deg = (sqrt(2))/2/(sqrt(2)) r = 1/(x ^ 2 * sqrt(2)) p(x, y) r = 1 XAT Steps for finding exact values: 1) If angle greater than (360 deg) / 2 * pi find co-terminal angle 2) Identify the quadrant then use ASTC to determine positive or negative 3) Find reference angle "Remember: pi/4 4) Evaluate trig function Sin=y COS X tan sin CSC sy sin cot== Sin = sec = 1 cos = 1 x 90 ^ 6 pi/2 (1,0) 180 deg ordered pairs: (cos theta, sin theta) Examples: 1) sin 150 deg = 1/2 Quadrant: I Reference <= (30 deg)/(180 ^ - 150) 4) tan (sqrt(3))/3 (7pi)/6 = Quadrant: + Reference angle= pi/6 π 3 (01) (1/2, (sqrt(3))/2) sin CSC + S A All + II IN TC COS + sec ((sqrt(2))/2, (sqrt(2))/2) tan cot + T 1300 ((sqrt(3))/2, 1/2) (phi - 1) deg 2) cos 600 deg = (240 deg) Quadrant: 111 Reference angle= 60 deg 240-180 5) sec((- pi)/4) = boxed 2 4 Quadrant: IN Reference angle= 21/4 (1,0 0 360 deg 3) cos (3pi)/5 = (- sqrt(2))/2 QuadrantI Reference = A 6) cot 180°= undefined Quadrant: xaxis Reference = y undefined PRACTICE PROBLEMS: Find each EXACT value. Do NOT use a calculator!! Complete on a separate paper. 1) sin((5pi)/3) 5) an * 225 deg 9) tan 135 deg 2) sin 210 deg 3) cos (12pi)/6 4) sin 870 deg 6) csc 6 7) cos (- 10pi)/(7pi) ^ 3 8) an * 960 deg 10) csc (47pi)/6 11) 6 12) cot 240 deg 1/x = 1/(sqrt(2)) = 1/1 * 2/(sqrt(2)) = 2/(sqrt(2)) * (sqrt(2))/(sqrt(2)) = (2sqrt(2))/2 210 deg = (sqrt(3))/3 x/3 * 60 deg 45 deg