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

2020
Views:

106

Pages:

3
Author:

Nomes67i

PRE-CALCULUS/TRIGONOMETRY 3 5.3 SOLVING TRIG EQUATIONS Name Date: Block Warm-Up: Find the reference angles of the following 1.) 30 = 30 deg Q1:4 2.) 225 deg = 45 deg 0111.4-180 3.) 330 deg = 30 deg Q1V-360-4 4.) 120 deg = 60 deg Q11-180-4 8. (4pi)/3 = pi/3 09 * remember the trick for finding reference angles in radians: 5.) (11pi)/6 = pi/6 6. (2pi)/3 = pi/3 T: 90 S T:O 1.0.180 TC pi/4 = pi/4 (d ^ 2)/(dx), (d ^ 2)/(dx) root(1/2, 3), 7 * 15/3 per 01 T. 1) y = sin theta A = 1, p = 360 ^ 2 ,1+m.= 360 44 =90^ aligned = X vs X sin theta = 0 0.180360 01180K + 2) y = cos theta A= 1 4.p= 360^ 4 4. m = (360 ^ 4)/4 + 90 ^ 4 ,vs= X 80 ,vs= X 80 900 27030 40130 200 300 GOAL: isolate the trig function(s), set 0, solve for all angles that are that villue When the equation = 0, the solutions are the X-intercepts TIPS FOR SOLVING: If you have one "cos x", "sin x" or "tan x", get it by itself on one side. If you have two "cos x", "sin x" or "tan x", pull out a GCF and set factors equal to zero and solve. If you have a trinomial, factor and set each factor equal to zero and solve. If you have different trig functions (ex: sin and cos), change one of them to the other using identities or reason through the answer using their exact values. 180-44 Examples: 180+4 360-4 Solve the following trigonometric equations. Calculate all answers over the interval (0,360°]. 1) 2cos x - 1 = 0 (2cos x)/2 = 1/2 cos X = 1/2 x = 60 ^ 6, 300 ^ 6 COS++ GT, GN 2) 2sin x + sqrt(2) = 0 (2sin x)/2 = (- sqrt(2))/2 (z 2 = 45x * sin x = (- sqrt(2))/2 sin -4pi, GN X 225,315 3) 4cos^2 x - 3 = 0 (4cos^2 x)/4 = 3/4 cos^2 x = 3/4 cos X = plus/minus (sqrt(3))/2 X * 30 ,150^ c 210 deg, 330 deg ain Q! GIT. 180-30 180+30 Q: 360-30 S 4) 2cos^2 x + cos x = 0 cos x * (2cos x + 1) = 0 cos x = D(1is) * 2cos x + 1 = 0 x=90 1 deg 270^ 2c5X = - 1 1 2 cup (0) ^ 2 = cos x = - 1/2 (03-Q*Pi = 1 80^ -60 qnr * 101 60 X = 120 deg, 240 deg 7) x=90^ prime ,126^ prime ,24C^ prime ,290^ prime ] inx + sqrt(2) = - sin x + O_{0} * 1 = C_{0} 2sin x + sqrt(2) = 0 h2 2 = 45 deg * 8 - sqrt(2) - sqrt(2) (2sin x)/2 = (- sqrt(2))/2 sin x = (- sqrt(2))/2 QIⅢ: 180145 x =225^ prime prime ,315^ prime prime QIT 310-45 5) sin x - cos x = 0 sin x = cos x option 1. on the unit, 21:45 Circle dees sinx-c3x Q: spot (same valve, srime sign) x = 45, 225y uption 2: use iden ti ties. sin x = cos x a*n_{x} + tan x = 1 underline x =45^ prime prime ,225^ prime 8) 2sin^2 x = cos x + 1 triguse idenh tres. 2(1 - cos^2 x) = cos x + 1 1 - 2cos^2 x = cos x + 1 12cos - x + 2cos^2 x - 2 0 = 2cos^2 x + cos x - 1 0 = (2cos x - 1)(cos x + 1) 2cos x - 1 = 0 2cos x * 3x = 1/2 Cospes Q1. 60 cos X = 1/2 x = 60 deg, 300 deg cos* rl = 0 cos x = - i * (axi * 5) x = 180 deg 6) cos^2 x - 2cos x + 1 = 0 cos x-1) (cos x - 1) = 0 cos x - 1 = 0 cos x = I(axis) x + 0 deg, 360' 9 sin^7 x + 4sin x + 3 = 0 (sin x + 3)(sin x + 1) = 0 Sinx+1=0 33 sin x = - 3 -1-1 sin x = J_{15} Ø X = 270 deg x = 60 ^ 2, 180 ^ 2, 300 deg