What is the general solution for -6sec(θ)-3=-15 ?

The general solution for -6sec(θ)-3=-15 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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-6sec(θ)-3=-15

- 6 sec (θ) - 3 = - 15

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

- 6 sec (θ) - 3 = - 15

Move

3

to the right side

- 6 sec (θ) - 3 = - 15

Add

3

to both sides

- 6 sec (θ) - 3 + 3 = - 15 + 3

Simplify

- 6 sec (θ) = - 12

- 6 sec (θ) = - 12

Divide both sides by

- 6

- 6 sec (θ) = - 12

Divide both sides by

- 6

\frac{- 6 sec ( θ )}{- 6} = \frac{- 12}{- 6}

Simplify

\frac{- 6 sec ( θ )}{- 6} = \frac{- 12}{- 6}

Simplify

\frac{- 6 sec ( θ )}{- 6} : sec (θ)

\frac{- 6 sec ( θ )}{- 6}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{6 sec ( θ )}{6}

Divide the numbers:

\frac{6}{6} = 1

= sec (θ)

Simplify

\frac{- 12}{- 6} : 2

\frac{- 12}{- 6}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{12}{6}

Divide the numbers:

\frac{12}{6} = 2

= 2

sec (θ) = 2

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

15 cos (θ) = 7 + cos (θ)

2 cos (3 x) = 2

tan^{2} (\frac{x}{2}) - tan (\frac{x}{2}) - 2 = 0

tan (x) = \frac{- 3}{4}

sin (x) = - 2 sin^{2} (x)

What is the general solution for -6sec(θ)-3=-15 ?
The general solution for -6sec(θ)-3=-15 is θ= pi/3+2pin,θ=(5pi)/3+2pin