What is the general solution for 3sqrt(2)sec(θ)+7=1 ?

The general solution for 3sqrt(2)sec(θ)+7=1 is θ=(3pi)/4+2pin,θ=(5pi)/4+2pin

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Popular >

3sqrt(2)sec(θ)+7=1

Solution

32 sec (θ) + 7 = 1

Solution

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Degrees

θ = 13 5^{\circ} + 36 0^{\circ} n, θ = 22 5^{\circ} + 36 0^{\circ} n

Solution steps

32 sec (θ) + 7 = 1

Move

7

to the right side

32 sec (θ) + 7 = 1

Subtract

7

from both sides

32 sec (θ) + 7 - 7 = 1 - 7

Simplify

32 sec (θ) = - 6

32 sec (θ) = - 6

Divide both sides by

32

32 sec (θ) = - 6

Divide both sides by

32

\frac{3 2 sec ( θ )}{3 2} = \frac{- 6}{3 2}

Simplify

\frac{3 2 sec ( θ )}{3 2} = \frac{- 6}{3 2}

Simplify

\frac{3 2 sec ( θ )}{3 2} : sec (θ)

\frac{3 2 sec ( θ )}{3 2}

Divide the numbers:

\frac{3}{3} = 1

= \frac{2 sec ( θ )}{2}

Cancel the common factor:

2

= sec (θ)

Simplify

\frac{- 6}{3 2} : - 2

\frac{- 6}{3 2}

Apply the fraction rule:

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

= - \frac{6}{3 2}

Divide the numbers:

\frac{6}{3} = 2

= \frac{2}{2}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{2}{2 ^{\frac{1}{2}}}

Apply exponent rule:

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

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= 2^{1 - \frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 2^{\frac{1}{2}}

Apply radical rule:

2^{\frac{1}{2}} = 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{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

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4cos^2(x)+4=6

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sin(2x+pi/6)=-1/2

sin (2 x + \frac{π}{6}) = - \frac{1}{2}

sin(θ)=-(sqrt(11))/6

sin (θ) = - \frac{11}{6}

Frequently Asked Questions (FAQ)

What is the general solution for 3sqrt(2)sec(θ)+7=1 ?
The general solution for 3sqrt(2)sec(θ)+7=1 is θ=(3pi)/4+2pin,θ=(5pi)/4+2pin