What is the general solution for 4sec(θ)+1=9 ?

The general solution for 4sec(θ)+1=9 is θ= pi/3+2pin,θ=(5pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4sec(θ)+1=9

4 sec (θ) + 1 = 9

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

Degrees

θ = 6 0^{\circ} + 36 0^{\circ} n, θ = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

4 sec (θ) + 1 = 9

Move

1

to the right side

4 sec (θ) + 1 = 9

Subtract

1

from both sides

4 sec (θ) + 1 - 1 = 9 - 1

Simplify

4 sec (θ) = 8

4 sec (θ) = 8

Divide both sides by

4

4 sec (θ) = 8

Divide both sides by

4

\frac{4 sec ( θ )}{4} = \frac{8}{4}

Simplify

sec (θ) = 2

sec (θ) = 2

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

4 tan^{2} (x) - 12 = 0

tan (θ) - \frac{1}{3} = 0

tan (\frac{x}{2} + \frac{π}{3}) = 1

- cot (x) + csc (x) = 1

cot (\frac{x}{2}) = 0

What is the general solution for 4sec(θ)+1=9 ?
The general solution for 4sec(θ)+1=9 is θ= pi/3+2pin,θ=(5pi)/3+2pin