Solving Trig Equations Multiple Angles

Find the first two non-negative solutions in radians 2cos(3x)+4=5

Use a calculator to solve for both angles on the interval [0,360) Round to the nearest tenth of a degree.

solve: 4cos²x = 3

• 30°, 300°

• 30°, 150°, 210°, 330°

• 60°, 120°

• 60°, 120°, 240°, 300°

solve: 2sin(x/2) = 1

• 60°, 300°

• 60°, 120°

• 300°, 330°

• 210°, 330°

If cosΘ = -1/2, what does theta equal? There are two answers, put the smaller answer first (a)   and ​ (b)  

• 240

• 330

• 45

• 60

• 360

• 120

• 135

• 345

• 210

• 225

Answer explanation

cosine correlates with x values and there are only two points on the unit circle with an x value of -1/2 and they are 240 and 120

Solve for x.

• 24.20

• 4.92

• 290.4

• 29.75

For what numbers x, 0≤x≤2π, does sin x =1

• π/2, 3π/2

• π/2

• 0, 2

• none

For what numbers x, 0 e x e2 ext{π} , does sin x= -1

• π/2, 3π/2

• 3π/2

• none

For what numbers x, 0 e x e2 ext{π}, does sin x= -1

• π/2, 3π/2

• 3π/2

• none

For what numbers x, 0 e x e2 \pi, does sin x =1

• π/2, 3π/2

• π/2

• 0, 2

• none