What is the general solution for sec^2(x)= 4/3 ,0<= x<= 2pi ?

Q: What is the general solution for sec^2(x)= 4/3 ,0<= x<= 2pi ?

The general solution for sec^2(x)= 4/3 ,0<= x<= 2pi is x= pi/6 ,x=(11pi)/6 ,x=(5pi)/6 ,x=(7pi)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec^2(x)= 4/3 ,0<= x<= 2pi

Solution

sec^{2} (x) = \frac{4}{3}, 0 \leq x \leq 2 π

Solution

x = \frac{π}{6}, x = \frac{11 π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}

Degrees

x = 3 0^{\circ}, x = 33 0^{\circ}, x = 15 0^{\circ}, x = 21 0^{\circ}

Solution steps

sec^{2} (x) = \frac{4}{3}, 0 \leq x \leq 2 π

Solve by substitution

sec^{2} (x) = \frac{4}{3}

Let:

sec (x) = u

u^{2} = \frac{4}{3}

u^{2} = \frac{4}{3} : u = \frac{2 3}{3}, u = - \frac{2 3}{3}

u^{2} = \frac{4}{3}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = \frac{4}{3}, u = - \frac{4}{3}

\frac{4}{3} = \frac{2 3}{3}

\frac{4}{3}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{4}{3}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{2}{3}

Rationalize

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

= \frac{2 3}{3}

- \frac{4}{3} = - \frac{2 3}{3}

- \frac{4}{3}

Simplify

\frac{4}{3} : \frac{2}{3}

\frac{4}{3}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{4}{3}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{2}{3}

= - \frac{2}{3}

Rationalize

- \frac{2}{3} : - \frac{2 3}{3}

- \frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

= - \frac{2 3}{3}

u = \frac{2 3}{3}, u = - \frac{2 3}{3}

Substitute back

u = sec (x)

sec (x) = \frac{2 3}{3}, sec (x) = - \frac{2 3}{3}

sec (x) = \frac{2 3}{3}, sec (x) = - \frac{2 3}{3}

sec (x) = \frac{2 3}{3}, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{11 π}{6}

sec (x) = \frac{2 3}{3}, 0 \leq x \leq 2 π

General solutions for

sec (x) = \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}

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

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

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{11 π}{6}

sec (x) = - \frac{2 3}{3}, 0 \leq x \leq 2 π : x = \frac{5 π}{6}, x = \frac{7 π}{6}

sec (x) = - \frac{2 3}{3}, 0 \leq x \leq 2 π

General solutions for

sec (x) = - \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}

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Solutions for the range

0 \leq x \leq 2 π

x = \frac{5 π}{6}, x = \frac{7 π}{6}

Combine all the solutions

x = \frac{π}{6}, x = \frac{11 π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}

Popular Examples

sqrt(3)tan(3θ)-1=0

3 tan (3 θ) - 1 = 0

2tan(x)=sec(x)

2 tan (x) = sec (x)

cos(x)=2pi

cos (x) = 2 π

sin(6x)+sin(2x)=0

sin (6 x) + sin (2 x) = 0

cos(a)=-1/2

cos (a) = - \frac{1}{2}

Frequently Asked Questions (FAQ)

What is the general solution for sec^2(x)= 4/3 ,0<= x<= 2pi ?
The general solution for sec^2(x)= 4/3 ,0<= x<= 2pi is x= pi/6 ,x=(11pi)/6 ,x=(5pi)/6 ,x=(7pi)/6