Solving Trig Equations

Category 1

100

sin(x)+2^½=-sin(x) What does x equal?

x=5pi/4 and 7pi/4 Work: 2sin(x)=-(2)^½ sin(x)=-(2)^1/2/(2) x=5pi/4 and 7pi/4

200

3tan^2x=1 What does tans equal?

Tanx=+- 1/root3

300

2(cosx+1)=1 Solve for X

X=2pi/3, 4pi/3 Work shown: 2cosx+2=1 2cosx=-1 cosx=-1/2 Cosine is negative in Quadrants II and III Cosx=1/2 is reference angle of 60 degrees or pi/3

400

4tanx+2=2tanx Solve for x in degrees

X= 135 degrees, 315 degrees Work: 2tanx=-2 tanx=-1 tan<0 in quadrants II and IV Tanx=1 has reference angle of 45 degrees

Category 2

100

2sinx - 1 = 0 Solve for sinx

sinx = .5 sin π/6 =½ sin 5π/6 = ½

200

Tan^2x-3=0 Solve for x X [0,pi]

X=pi/3 (60 degrees) and x= 2pi/3 (120 degrees) Work: tan^2x-3=0 tan^2x =3 tanx=+-root 3

300

tanxsin^2x=2tanx Solve for sinx and tanx x [0,2pi]

sinx=+-root2 tanx=0 Work: tanxsin^2x-2tanx=0 tanx(sin^2x-2)=0

400

2cosx+3=0 Solve for cosx

No solution because -1

Category 3

100

3(cosx-1)=3-4cosx Solve for x

x=31 degrees and 329 degrees Work: 7cosx=6 cosx=6/7 cos>0 in quadrants I and IV

200

2sin^2x+sinx-1=0 Solve for x x [0,2pi]

x=pi/6 or 5pi/6 and3pi/2 30 degrees, 150 degrees, 270 degrees

300

2cos^2x+3sinx-3=0 Solve for x in radians x [0,2pi]

X= pi/6 or 5pi/6 and pi/2