What is the general solution for 1/(cos(θ))=2 ?

The general solution for 1/(cos(θ))=2 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

1/(cos(θ))=2

\frac{1}{cos ( θ )} = 2

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

\frac{1}{cos ( θ )} = 2

Multiply both sides by

cos (θ)

\frac{1}{cos ( θ )} = 2

Multiply both sides by

cos (θ)

\frac{1}{cos ( θ )} cos (θ) = 2 cos (θ)

Simplify

1 = 2 cos (θ)

1 = 2 cos (θ)

Switch sides

2 cos (θ) = 1

Divide both sides by

2

2 cos (θ) = 1

Divide both sides by

2

\frac{2 cos ( θ )}{2} = \frac{1}{2}

Simplify

cos (θ) = \frac{1}{2}

cos (θ) = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

cos (θ) = 0

Take the denominator(s) of

\frac{1}{cos ( θ )}

and compare to zero

cos (θ) = 0

The following points are undefined

cos (θ) = 0

Combine undefined points with solutions:

cos (θ) = \frac{1}{2}

General solutions for

cos (θ) = \frac{1}{2}

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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