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

2020
Views:

32

Pages:

5
Author:

princesa035c6tg

Pre-Calculus/Trig 3 UNIT 7: Trigonometric identities & Equations-SECTION 5 WORKSHEET #1 Name: KEY Date: SOLVING TRIGONOMETRIC EQUATIONS Directions: Solve each trigonometric function for ALL POSSIBLE VALUES IN DEGREES. Use the hints provided. HINT COLLECT LIKE TERMS HINT EXTRACT SQUARE ROOTS 1.) cos x + sqrt(3) = - cos x 2.) 4sin^2 theta - 3 = 0 2cos x + sqrt(3) + 0 2cos x = - sqrt(3) cos x = - (sqrt(3))/2 x - 150 deg 210 x = 150 + 360k X = 210 + 360k 4sin^2 theta = 3 sin^d theta = sqrt(3/4) sin theta + t * (sqrt(3))/2 * 14 deg fou theta = 60 deg * 120 deg 240, 300 deg theta = 60 deg * 180K Theta = a * 40 deg + 180k Directions: Solve each trigonometric function for ALL POSSIBLE VALUES IN RADIANS. Use the hints provided. HINT FACTOR GCF 3.) 2cos theta * sin theta = cos theta 2cos theta4. n*theta - cos theta = 0 cos theta * (2sin theta - 1) = 0 cos theta = 0 theta = pi/2, (3pi)/2 sin theta - 1 = 0 sin theta = 1/2 theta = theta = sqrt(6) * 2pi*k theta = pi/2 * pi*k (0,1) + SIT 3 - 1 G ( \mathfrak{o}, ∞ \ theta = 50/6 + 2pi*k HINT FACTOR EQUATION AS QUADRATIC TYPE 4.) 2sin^2 x - 3sin x + 1 = 0 (2sin x - 1)(sin x - 1) = 0 2sin x - 1 = 0 sin x = 1/2 x = pi/6, (5pi)/6 x = pi/6 + 2pi*k x = (5pi)/6 + 2pi*k 3inx - 1 = 0 5mx = 1 x - E K = pi/alpha + 2pi*k 10,11 Directions: Solve each trigonometric function IN THE INTERVAL [0,2π). Use the hints provided. HINT REWRITE WITH SINGLE TRIG FUNCTION 5.) 3sec^2 x - 2tan^2 x - 4 = 0 3(tan^2 x + i) - 2tan^2 x - 4 = 0 3tan^d x + 3 - 2tan^2 x - 4 = 0 tan^2 x - 1 = 0 tan^2 x - 1 tan x - (plus/minus 1) x = pi/4 (3pi)/4 (5pi)/4 (7pi)/4 HINT SQUARE & CONVERT TO QUADRATIC TYPE CHECK FOR EXTRANEOUS SOWTIAN'S! 6.) (sin theta + 1) ^ alpha * (cos theta) ^ beta_{c} sin^2 theta + 2sin theta + 1 - cos^2 theta sin^2 theta + 2sin theta - 1 = 1 - sin^2 theta 2sin^d theta + d * sin theta = 0 2sin theta * (sin theta + 1) = 0 2a * sin theta = 0 sin theta = 0 5 ,n 6+1=0 theta = 0 sint-1 theta - (3pi)/2 \ - 1 ,*) LEXTRANEWS! (10) (۵۱) Directions: Solve each trigonometric function IN THE INTERVAL [0,360). Use the hints provided. HINT FUNCTIONS OF MULTIPLE ANGLES HINT USING INVERSE FUNCTIONS (calculator) 7.) sin 2x - (sqrt(3))/2 = 0 sin 2x - (sqrt(3))/2 Ser 4x = 13 sin theta = (sqrt(3))/2 theta * 40 ^ 4 2x - 60 x - 30 2x = 120 X - 60 120 deg 8.) 4tan^2 theta + 5tan theta = 6 4tan^2 theta + 5tan theta - 6 = 0 (4tan theta - 3)(tan theta + 2) = 0 4sin theta - 3 = 0 tan theta = 3/4 theta = arctan(S/4) theta = 36.9 deg tan theta + 2 = 0 tan theta = - 2 theta = arctan(- lambda) 6 ^ - -63.4^ + 56 * 9 2u + 1 Q = 36, 9 deg 216.9. 110.16 246 ماء 0-116.6°, 246.6