What is the general solution for sec(3x)=5 ?

The general solution for sec(3x)=5 is x=(1.36943…)/3+(2pin)/3 ,x=(2pi)/3-(1.36943…)/3+(2pin)/3

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sec(3x)=5

sec (3 x) = 5

x = \frac{1.36943 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.36943 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 26.15434 \dots^{\circ} + 12 0^{\circ} n, x = 93.84565 \dots^{\circ} + 12 0^{\circ} n

Solution steps

sec (3 x) = 5

Apply trig inverse properties

sec (3 x) = 5

General solutions for

sec (3 x) = 5

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

3 x = arcsec (5) + 2 πn, 3 x = 2 π - arcsec (5) + 2 πn

3 x = arcsec (5) + 2 πn, 3 x = 2 π - arcsec (5) + 2 πn

Solve

3 x = arcsec (5) + 2 πn : x = \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

3 x = arcsec (5) + 2 πn

Divide both sides by

3

3 x = arcsec (5) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

x = \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

Solve

3 x = 2 π - arcsec (5) + 2 πn : x = \frac{2 π}{3} - \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

3 x = 2 π - arcsec (5) + 2 πn

Divide both sides by

3

3 x = 2 π - arcsec (5) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{2 π}{3} - \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

x = \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arcsec ( 5 )}{3} + \frac{2 πn}{3}

Show solutions in decimal form

x = \frac{1.36943 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.36943 \dots}{3} + \frac{2 πn}{3}

3 sin^{2} (x) + 2 sin (x) cos^{2} (\frac{x}{2}) - sin (x) = 0

3 tan^{2} (y) = 5 sec (y) - 1

\frac{( 1 - tan ^{2} ( a ) )}{( tan ( a ) )} = 2 cot^{2} (a)

cos (6 x) = cos (2 x)

cot (x) cos (x) - sin (x) = 1

What is the general solution for sec(3x)=5 ?
The general solution for sec(3x)=5 is x=(1.36943…)/3+(2pin)/3 ,x=(2pi)/3-(1.36943…)/3+(2pin)/3