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

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

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1/(cos(θ))=1

\frac{1}{cos ( θ )} = 1

θ = 2 πn

Degrees

θ = 0^{\circ} + 36 0^{\circ} n

Solution steps

\frac{1}{cos ( θ )} = 1

Multiply both sides by

cos (θ)

\frac{1}{cos ( θ )} = 1

Multiply both sides by

cos (θ)

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

Simplify

1 = cos (θ)

1 = cos (θ)

Switch sides

cos (θ) = 1

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) = 1

General solutions for

cos (θ) = 1

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 = 0 + 2 πn

θ = 0 + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn

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