What is the general solution for -3sec(θ/3)=-3sqrt(2) ?

The general solution for -3sec(θ/3)=-3sqrt(2) is θ=(3pi)/4+6pin,θ=(21pi)/4+6pin

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Popular >

-3sec(θ/3)=-3sqrt(2)

Solution

- 3 sec (\frac{θ}{3}) = - 32

Solution

θ = \frac{3 π}{4} + 6 πn, θ = \frac{21 π}{4} + 6 πn

Degrees

θ = 13 5^{\circ} + 108 0^{\circ} n, θ = 94 5^{\circ} + 108 0^{\circ} n

Solution steps

- 3 sec (\frac{θ}{3}) = - 32

Divide both sides by

- 3

- 3 sec (\frac{θ}{3}) = - 32

Divide both sides by

- 3

\frac{- 3 sec ( \frac{θ}{3} )}{- 3} = \frac{- 3 2}{- 3}

Simplify

\frac{- 3 sec ( \frac{θ}{3} )}{- 3} = \frac{- 3 2}{- 3}

Simplify

\frac{- 3 sec ( \frac{θ}{3} )}{- 3} : sec (\frac{θ}{3})

\frac{- 3 sec ( \frac{θ}{3} )}{- 3}

Apply the fraction rule:

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

= \frac{3 sec ( \frac{θ}{3} )}{3}

Divide the numbers:

\frac{3}{3} = 1

= sec (\frac{θ}{3})

Simplify

\frac{- 3 2}{- 3} : 2

\frac{- 3 2}{- 3}

Apply the fraction rule:

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

= \frac{3 2}{3}

Divide the numbers:

\frac{3}{3} = 1

= 2

sec (\frac{θ}{3}) = 2

sec (\frac{θ}{3}) = 2

sec (\frac{θ}{3}) = 2

General solutions for

sec (\frac{θ}{3}) = 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}

\frac{θ}{3} = \frac{π}{4} + 2 πn, \frac{θ}{3} = \frac{7 π}{4} + 2 πn

\frac{θ}{3} = \frac{π}{4} + 2 πn, \frac{θ}{3} = \frac{7 π}{4} + 2 πn

Solve

\frac{θ}{3} = \frac{π}{4} + 2 πn : θ = \frac{3 π}{4} + 6 πn

\frac{θ}{3} = \frac{π}{4} + 2 πn

Multiply both sides by

3

\frac{θ}{3} = \frac{π}{4} + 2 πn

Multiply both sides by

3

\frac{3 θ}{3} = 3 \cdot \frac{π}{4} + 3 \cdot 2 πn

Simplify

\frac{3 θ}{3} = 3 \cdot \frac{π}{4} + 3 \cdot 2 πn

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

3 \cdot \frac{π}{4} + 3 \cdot 2 πn : \frac{3 π}{4} + 6 πn

3 \cdot \frac{π}{4} + 3 \cdot 2 πn

Multiply

3 \cdot \frac{π}{4} : \frac{3 π}{4}

3 \cdot \frac{π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 3}{4}

= \frac{3 π}{4} + 3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= \frac{3 π}{4} + 6 πn

θ = \frac{3 π}{4} + 6 πn

θ = \frac{3 π}{4} + 6 πn

θ = \frac{3 π}{4} + 6 πn

Solve

\frac{θ}{3} = \frac{7 π}{4} + 2 πn : θ = \frac{21 π}{4} + 6 πn

\frac{θ}{3} = \frac{7 π}{4} + 2 πn

Multiply both sides by

3

\frac{θ}{3} = \frac{7 π}{4} + 2 πn

Multiply both sides by

3

\frac{3 θ}{3} = 3 \cdot \frac{7 π}{4} + 3 \cdot 2 πn

Simplify

\frac{3 θ}{3} = 3 \cdot \frac{7 π}{4} + 3 \cdot 2 πn

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

3 \cdot \frac{7 π}{4} + 3 \cdot 2 πn : \frac{21 π}{4} + 6 πn

3 \cdot \frac{7 π}{4} + 3 \cdot 2 πn

3 \cdot \frac{7 π}{4} = \frac{21 π}{4}

3 \cdot \frac{7 π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{7 π 3}{4}

Multiply the numbers:

7 \cdot 3 = 21

= \frac{21 π}{4}

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= 6 πn

= \frac{21 π}{4} + 6 πn

θ = \frac{21 π}{4} + 6 πn

θ = \frac{21 π}{4} + 6 πn

θ = \frac{21 π}{4} + 6 πn

θ = \frac{3 π}{4} + 6 πn, θ = \frac{21 π}{4} + 6 πn

Popular Examples

4cos(2x-pi)-1=1

4 cos (2 x - π) - 1 = 1

csc(x)=4sin(x)

csc (x) = 4 sin (x)

tan(3+x)=0

tan (3 + x) = 0

2cot^2(x)-9csc(x)=3

2 cot^{2} (x) - 9 csc (x) = 3

1=sin(2θ)

1 = sin (2 θ)

Frequently Asked Questions (FAQ)

What is the general solution for -3sec(θ/3)=-3sqrt(2) ?
The general solution for -3sec(θ/3)=-3sqrt(2) is θ=(3pi)/4+6pin,θ=(21pi)/4+6pin