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Popular >

0.2727=sec(2.746x)-1

Solution

0.2727 = sec (2.746 x) - 1

Solution

x = \frac{0.66691 \dots}{2.746} + \frac{2 πn}{2.746}, x = \frac{2 π}{2.746} - \frac{0.66691 \dots}{2.746} + \frac{2 πn}{2.746}

+1

Degrees

x = 13.91538 \dots^{\circ} + 131.09978 \dots^{\circ} n, x = 117.18439 \dots^{\circ} + 131.09978 \dots^{\circ} n

Solution steps

0.2727 = sec (2.746 x) - 1

Switch sides

sec (2.746 x) - 1 = 0.2727

Move

1

to the right side

sec (2.746 x) - 1 = 0.2727

Add

1

to both sides

sec (2.746 x) - 1 + 1 = 0.2727 + 1

Simplify

sec (2.746 x) = 1.2727

sec (2.746 x) = 1.2727

Apply trig inverse properties

sec (2.746 x) = 1.2727

General solutions for

sec (2.746 x) = 1.2727

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

2.746 x = arcsec (1.2727) + 2 πn, 2.746 x = 2 π - arcsec (1.2727) + 2 πn

2.746 x = arcsec (1.2727) + 2 πn, 2.746 x = 2 π - arcsec (1.2727) + 2 πn

Solve

2.746 x = arcsec (1.2727) + 2 πn : x = \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

2.746 x = arcsec (1.2727) + 2 πn

Divide both sides by

2.746

2.746 x = arcsec (1.2727) + 2 πn

Divide both sides by

2.746

\frac{2.746 x}{2.746} = \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

Simplify

x = \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

x = \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

Solve

2.746 x = 2 π - arcsec (1.2727) + 2 πn : x = \frac{2 π}{2.746} - \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

2.746 x = 2 π - arcsec (1.2727) + 2 πn

Divide both sides by

2.746

2.746 x = 2 π - arcsec (1.2727) + 2 πn

Divide both sides by

2.746

\frac{2.746 x}{2.746} = \frac{2 π}{2.746} - \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

Simplify

x = \frac{2 π}{2.746} - \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

x = \frac{2 π}{2.746} - \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

x = \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}, x = \frac{2 π}{2.746} - \frac{arcsec ( 1.2727 )}{2.746} + \frac{2 πn}{2.746}

Show solutions in decimal form

x = \frac{0.66691 \dots}{2.746} + \frac{2 πn}{2.746}, x = \frac{2 π}{2.746} - \frac{0.66691 \dots}{2.746} + \frac{2 πn}{2.746}

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