What is the general solution for 2sec(θ)+2=6 ?

The general solution for 2sec(θ)+2=6 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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2sec(θ)+2=6

2 sec (θ) + 2 = 6

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

2 sec (θ) + 2 = 6

Move

2

to the right side

2 sec (θ) + 2 = 6

Subtract

2

from both sides

2 sec (θ) + 2 - 2 = 6 - 2

Simplify

2 sec (θ) = 4

2 sec (θ) = 4

Divide both sides by

2

2 sec (θ) = 4

Divide both sides by

2

\frac{2 sec ( θ )}{2} = \frac{4}{2}

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 cos (x) tan (x) = 3 tan (x)

3 sin (x) = 1 + sin (x)

2 sin (x - \frac{π}{6}) + 1 = 0

3 - 3 sin (θ) = 6 cos^{2} (θ)

sin (x) + sin^{2} (x) + cos^{2} (x) = 1

What is the general solution for 2sec(θ)+2=6 ?
The general solution for 2sec(θ)+2=6 is θ= pi/3+2pin,θ=(5pi)/3+2pin