What is the general solution for (3sec(θ)-2sqrt(3))(2sin(θ)-1)=0,2pi ?

The general solution for (3sec(θ)-2sqrt(3))(2sin(θ)-1)=0,2pi is No Solution for θ\in\mathbb{R}

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Popular >

(3sec(θ)-2sqrt(3))(2sin(θ)-1)=0,2pi

Solution

(3 sec (θ) - 23) (2 sin (θ) - 1) = 0, 2 π

Solution

No Solution for θ \in R

Solution steps

(3 sec (θ) - 23) (2 sin (θ) - 1) = 0, 2 π

Solving each part separately

3 sec (θ) - 23 = 0 or 2 sin (θ) - 1 = 0

3 sec (θ) - 23 = 0, 2 π :

No Solution

3 sec (θ) - 23 = 0, 2 π

Move

23

to the right side

3 sec (θ) - 23 = 0

Add

23

to both sides

3 sec (θ) - 23 + 23 = 0 + 23

Simplify

3 sec (θ) = 23

3 sec (θ) = 23

Divide both sides by

3

3 sec (θ) = 23

Divide both sides by

3

\frac{3 sec ( θ )}{3} = \frac{2 3}{3}

Simplify

sec (θ) = \frac{2 3}{3}

sec (θ) = \frac{2 3}{3}

General solutions for

sec (θ) = \frac{2 3}{3}

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solutions for the range

2 π

No Solution

2 sin (θ) - 1 = 0, 2 π :

No Solution

2 sin (θ) - 1 = 0, 2 π

Move

1

to the right side

2 sin (θ) - 1 = 0

Add

1

to both sides

2 sin (θ) - 1 + 1 = 0 + 1

Simplify

2 sin (θ) = 1

2 sin (θ) = 1

Divide both sides by

2

2 sin (θ) = 1

Divide both sides by

2

\frac{2 sin ( θ )}{2} = \frac{1}{2}

Simplify

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

General solutions for

sin (θ) = \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solutions for the range

2 π

No Solution

Combine all the solutions

No Solution for θ \in R

Popular Examples

7cos(θ)-3=3sin^2(θ)

7 cos (θ) - 3 = 3 sin^{2} (θ)

cos(pi/6 t)=cos(pi/6 (t-3))

cos (\frac{π}{6} t) = cos (\frac{π}{6} (t - 3))

0=arcsin(sqrt(x))

0 = arcsin (x)

cos(2y)-sin(2y)=0

cos (2 y) - sin (2 y) = 0

sec((2pi)/3+x)=2

sec (\frac{2 π}{3} + x) = 2

Frequently Asked Questions (FAQ)

What is the general solution for (3sec(θ)-2sqrt(3))(2sin(θ)-1)=0,2pi ?
The general solution for (3sec(θ)-2sqrt(3))(2sin(θ)-1)=0,2pi is No Solution for θ\in\mathbb{R}