What is the general solution for sec(2x+60)=-1.5 ?

The general solution for sec(2x+60)=-1.5 is x=-30+pin+(2.30052…)/2 ,x=-30+pin-(2.30052…)/2

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sec(2x+60)=-1.5

Solution

sec (2 x + 60) = - 1.5

Solution

x = - 30 + πn + \frac{2.30052 \dots}{2}, x = - 30 + πn - \frac{2.30052 \dots}{2}

Degrees

x = - 1652.96822 \dots^{\circ} + 18 0^{\circ} n, x = - 1784.77854 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sec (2 x + 60) = - 1.5

Apply trig inverse properties

sec (2 x + 60) = - 1.5

General solutions for

sec (2 x + 60) = - 1.5

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

2 x + 60 = arcsec (- 1.5) + 2 πn, 2 x + 60 = - arcsec (- 1.5) + 2 πn

2 x + 60 = arcsec (- 1.5) + 2 πn, 2 x + 60 = - arcsec (- 1.5) + 2 πn

Solve

2 x + 60 = arcsec (- 1.5) + 2 πn : x = - 30 + πn + \frac{arcsec ( - 1.5 )}{2}

2 x + 60 = arcsec (- 1.5) + 2 πn

Move

60

to the right side

2 x + 60 = arcsec (- 1.5) + 2 πn

Subtract

60

from both sides

2 x + 60 - 60 = arcsec (- 1.5) + 2 πn - 60

Simplify

2 x = arcsec (- 1.5) + 2 πn - 60

2 x = arcsec (- 1.5) + 2 πn - 60

Divide both sides by

2

2 x = arcsec (- 1.5) + 2 πn - 60

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsec ( - 1.5 )}{2} + \frac{2 πn}{2} - \frac{60}{2}

Simplify

\frac{2 x}{2} = \frac{arcsec ( - 1.5 )}{2} + \frac{2 πn}{2} - \frac{60}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{arcsec ( - 1.5 )}{2} + \frac{2 πn}{2} - \frac{60}{2} : - 30 + πn + \frac{arcsec ( - 1.5 )}{2}

\frac{arcsec ( - 1.5 )}{2} + \frac{2 πn}{2} - \frac{60}{2}

Group like terms

= - \frac{60}{2} + \frac{2 πn}{2} + \frac{arcsec ( - 1.5 )}{2}

Divide the numbers:

\frac{60}{2} = 30

= - 30 + \frac{2 πn}{2} + \frac{arcsec ( - 1.5 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= - 30 + πn + \frac{arcsec ( - 1.5 )}{2}

x = - 30 + πn + \frac{arcsec ( - 1.5 )}{2}

x = - 30 + πn + \frac{arcsec ( - 1.5 )}{2}

x = - 30 + πn + \frac{arcsec ( - 1.5 )}{2}

Solve

2 x + 60 = - arcsec (- 1.5) + 2 πn : x = - 30 + πn - \frac{arcsec ( - 1.5 )}{2}

2 x + 60 = - arcsec (- 1.5) + 2 πn

Move

60

to the right side

2 x + 60 = - arcsec (- 1.5) + 2 πn

Subtract

60

from both sides

2 x + 60 - 60 = - arcsec (- 1.5) + 2 πn - 60

Simplify

2 x = - arcsec (- 1.5) + 2 πn - 60

2 x = - arcsec (- 1.5) + 2 πn - 60

Divide both sides by

2

2 x = - arcsec (- 1.5) + 2 πn - 60

Divide both sides by

2

\frac{2 x}{2} = - \frac{arcsec ( - 1.5 )}{2} + \frac{2 πn}{2} - \frac{60}{2}

Simplify

\frac{2 x}{2} = - \frac{arcsec ( - 1.5 )}{2} + \frac{2 πn}{2} - \frac{60}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

- \frac{arcsec ( - 1.5 )}{2} + \frac{2 πn}{2} - \frac{60}{2} : - 30 + πn - \frac{arcsec ( - 1.5 )}{2}

- \frac{arcsec ( - 1.5 )}{2} + \frac{2 πn}{2} - \frac{60}{2}

Group like terms

= - \frac{60}{2} + \frac{2 πn}{2} - \frac{arcsec ( - 1.5 )}{2}

Divide the numbers:

\frac{60}{2} = 30

= - 30 + \frac{2 πn}{2} - \frac{arcsec ( - 1.5 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= - 30 + πn - \frac{arcsec ( - 1.5 )}{2}

x = - 30 + πn - \frac{arcsec ( - 1.5 )}{2}

x = - 30 + πn - \frac{arcsec ( - 1.5 )}{2}

x = - 30 + πn - \frac{arcsec ( - 1.5 )}{2}

x = - 30 + πn + \frac{arcsec ( - 1.5 )}{2}, x = - 30 + πn - \frac{arcsec ( - 1.5 )}{2}

Show solutions in decimal form

x = - 30 + πn + \frac{2.30052 \dots}{2}, x = - 30 + πn - \frac{2.30052 \dots}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for sec(2x+60)=-1.5 ?
The general solution for sec(2x+60)=-1.5 is x=-30+pin+(2.30052…)/2 ,x=-30+pin-(2.30052…)/2