What is the general solution for sec(4x)-9=0 ?

The general solution for sec(4x)-9=0 is x=(1.45945…)/4+(pin)/2 ,x= pi/2-(1.45945…)/4+(pin)/2

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Popular >

sec(4x)-9=0

Solution

sec (4 x) - 9 = 0

Solution

x = \frac{1.45945 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{1.45945 \dots}{4} + \frac{πn}{2}

Degrees

x = 20.90515 \dots^{\circ} + 9 0^{\circ} n, x = 69.09484 \dots^{\circ} + 9 0^{\circ} n

Solution steps

sec (4 x) - 9 = 0

Move

9

to the right side

sec (4 x) - 9 = 0

Add

9

to both sides

sec (4 x) - 9 + 9 = 0 + 9

Simplify

sec (4 x) = 9

sec (4 x) = 9

Apply trig inverse properties

sec (4 x) = 9

General solutions for

sec (4 x) = 9

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

4 x = arcsec (9) + 2 πn, 4 x = 2 π - arcsec (9) + 2 πn

4 x = arcsec (9) + 2 πn, 4 x = 2 π - arcsec (9) + 2 πn

Solve

4 x = arcsec (9) + 2 πn : x = \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

4 x = arcsec (9) + 2 πn

Divide both sides by

4

4 x = arcsec (9) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

Solve

4 x = 2 π - arcsec (9) + 2 πn : x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

4 x = 2 π - arcsec (9) + 2 πn

Divide both sides by

4

4 x = 2 π - arcsec (9) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{2 π}{4} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

Cancel

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{2 πn}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

x = \frac{arcsec ( 9 )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arcsec ( 9 )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.45945 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{1.45945 \dots}{4} + \frac{πn}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for sec(4x)-9=0 ?
The general solution for sec(4x)-9=0 is x=(1.45945…)/4+(pin)/2 ,x= pi/2-(1.45945…)/4+(pin)/2