5.3 Solving Trig Equations by RHO

30°, 150°

Find all values of x in the interval 0 ≤ x < 360° such that 2sin²x + 5sinx - 3 = 0

π/6, 11π/6

Solve 2cosx - √3 = 0 in the interval 0 ≤ x < 2π

π/6, 5π/6, 3π/2

Solve 2sin²x + sinx = 1 in the interval 0 ≤ x < 2π

π/3 and 4π/3

Solve 2tanx - √3 = tanx in the interval 0 ≤ x < 2π

π/6 + 2πn and 5π/6 + 2πn

Solve 4tan²x - 1 = tan²x

π

Solve cos x = −1 in the interval 0 ≤ x < 2π.

−90°, 90°

Solve cos θ = 0 in the interval −180° ≤ θ ≤ 180°.

3π/2

Solve cos(x/3) = 0 in the interval 0 ≤ x < 2π

π/2, π/6, 5π/6, 3π/2

Solve cosx = 2sinx cosx in the interval 0 ≤ x < 2π (HINT: set = 0, then factor GCF)

5π/6, 11π/6

Solve √3tanx + 1 = 0 in the interval 0 ≤ x < 2π

π/6 + 2π and 5π/6 + 2πn

Find all solutions to 2sin x - 1 = 0

π/3 + πn

Find all solutions to 3√(3)cot(x)=3

π/12 + πn/2 and 5π/12 + πn/2

Find all solutions to 4cos²(2x) - 3 = 0

π/3 + 2πn and 5π/3 + 2πn

Find all solutions to csc(x)-2cot(x)=0

π/2 + 2πn

Find all solutions to sin²x + sinx = 2

3π/4 +πn

Find all solutions to tanx + 1 = 0

120°, 240°

Find all values of x in the interval 0 ≤ x < 360° such that 2cos²x - 3cosx = 2

30°, 150°, 210°, 330°

Find all values of x in the interval 0 ≤ x < 360° such that 4cos²x - 3 = 0

π/4, 3π/4,5π/4, 7π/4

Solve 4 cos²x -2 = 0 in the interval 0 ≤ x < 2π

5π/6 , 7π/6

Solve for 0 ≤ x < 2π: 2cosx + √3 = 0

0

Solve for 0 ≤ x < 2π: 4 cosx - 3 = 1

0, π

Solve for 0 ≤ x < 2π: sinx cosx - 3sinx = 0

0, 2π/3, 4π/3

Solve for 0 ≤x < 2π : 2cos²x - cosx = 1

3π/4 and 5π/4

Solve √2cosx + 1 = 0 in the interval 0 ≤ x < 2π

πn and 3π/2 +2πn

Solve sin²x + sinx = 0

π/4 and 5π/4

Solve tan²x = tan x in the interval 0 ≤ x < 2π

5π/24 + πn/2 and 7π/24 + πn/2

Find all solutions to 2cos(4x) + √3 = 0