What is the general solution for sec^2(θ)-4=0,0<= θ<= 2pi ?

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

The general solution for sec^2(θ)-4=0,0<= θ<= 2pi is θ= pi/3 ,θ=(5pi)/3 ,θ=(2pi)/3 ,θ=(4pi)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec^2(θ)-4=0,0<= θ<= 2pi

Solution

sec^{2} (θ) - 4 = 0, 0 \leq θ \leq 2 π

Solution

θ = \frac{π}{3}, θ = \frac{5 π}{3}, θ = \frac{2 π}{3}, θ = \frac{4 π}{3}

Degrees

θ = 6 0^{\circ}, θ = 30 0^{\circ}, θ = 12 0^{\circ}, θ = 24 0^{\circ}

Solution steps

sec^{2} (θ) - 4 = 0, 0 \leq θ \leq 2 π

Solve by substitution

sec^{2} (θ) - 4 = 0

Let:

sec (θ) = u

u^{2} - 4 = 0

u^{2} - 4 = 0 : u = 2, u = - 2

u^{2} - 4 = 0

Move

4

to the right side

u^{2} - 4 = 0

Add

4

to both sides

u^{2} - 4 + 4 = 0 + 4

Simplify

u^{2} = 4

u^{2} = 4

For

x^{2} = f (a)

the solutions are

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

u = 4, u = - 4

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

- 4 = - 2

- 4

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= - 2

u = 2, u = - 2

Substitute back

u = sec (θ)

sec (θ) = 2, sec (θ) = - 2

sec (θ) = 2, sec (θ) = - 2

sec (θ) = 2, 0 \leq θ \leq 2 π : θ = \frac{π}{3}, θ = \frac{5 π}{3}

sec (θ) = 2, 0 \leq θ \leq 2 π

General solutions for

sec (θ) = 2

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}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solutions for the range

0 \leq θ \leq 2 π

θ = \frac{π}{3}, θ = \frac{5 π}{3}

sec (θ) = - 2, 0 \leq θ \leq 2 π : θ = \frac{2 π}{3}, θ = \frac{4 π}{3}

sec (θ) = - 2, 0 \leq θ \leq 2 π

General solutions for

sec (θ) = - 2

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{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Solutions for the range

0 \leq θ \leq 2 π

θ = \frac{2 π}{3}, θ = \frac{4 π}{3}

Combine all the solutions

θ = \frac{π}{3}, θ = \frac{5 π}{3}, θ = \frac{2 π}{3}, θ = \frac{4 π}{3}

Popular Examples

-sin(pi/2)

- sin (\frac{π}{2})

tan((5pi)/(12))

tan (\frac{5 π}{12})

cos(20)

cos (2 0^{\circ})

arcsec(1)

arcsec (1)

2cos^2(x)+3cos(x)-2=0

2 cos^{2} (x) + 3 cos (x) - 2 = 0

Frequently Asked Questions (FAQ)

What is the general solution for sec^2(θ)-4=0,0<= θ<= 2pi ?
The general solution for sec^2(θ)-4=0,0<= θ<= 2pi is θ= pi/3 ,θ=(5pi)/3 ,θ=(2pi)/3 ,θ=(4pi)/3