What is the general solution for solvefor y,x=sec(1/y) ?

The general solution for solvefor y,x=sec(1/y) is y= 1/(arcsec(x)+2pin),y= 1/(-arcsec(x)+2pin)

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Popular Trigonometry >

solvefor y,x=sec(1/y)

Solution

solve for

y, x = sec (\frac{1}{y})

Solution

y = \frac{1}{arcsec ( x ) + 2 πn}, y = \frac{1}{- arcsec ( x ) + 2 πn}

Solution steps

x = sec (\frac{1}{y})

Switch sides

sec (\frac{1}{y}) = x

Apply trig inverse properties

sec (\frac{1}{y}) = x

General solutions for

sec (\frac{1}{y}) = x

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

\frac{1}{y} = arcsec (x) + 2 πn, \frac{1}{y} = - arcsec (x) + 2 πn

\frac{1}{y} = arcsec (x) + 2 πn, \frac{1}{y} = - arcsec (x) + 2 πn

Solve

\frac{1}{y} = arcsec (x) + 2 πn : y = \frac{1}{arcsec ( x ) + 2 πn}

\frac{1}{y} = arcsec (x) + 2 πn

Multiply both sides by

y

\frac{1}{y} = arcsec (x) + 2 πn

Multiply both sides by

y

\frac{1}{y} y = arcsec (x) y + 2 πn y

Simplify

1 = arcsec (x) y + 2 πn y

1 = arcsec (x) y + 2 πn y

Switch sides

arcsec (x) y + 2 πn y = 1

Factor

arcsec (x) y + 2 πn y : y (arcsec (x) + 2 πn)

arcsec (x) y + 2 πn y

Factor out common term

y

= y (arcsec (x) + 2 πn)

y (arcsec (x) + 2 πn) = 1

Divide both sides by

arcsec (x) + 2 πn

y (arcsec (x) + 2 πn) = 1

Divide both sides by

arcsec (x) + 2 πn

\frac{y ( arcsec ( x ) + 2 πn )}{arcsec ( x ) + 2 πn} = \frac{1}{arcsec ( x ) + 2 πn}

Simplify

y = \frac{1}{arcsec ( x ) + 2 πn}

y = \frac{1}{arcsec ( x ) + 2 πn}

Solve

\frac{1}{y} = - arcsec (x) + 2 πn : y = \frac{1}{- arcsec ( x ) + 2 πn}

\frac{1}{y} = - arcsec (x) + 2 πn

Multiply both sides by

y

\frac{1}{y} = - arcsec (x) + 2 πn

Multiply both sides by

y

\frac{1}{y} y = - arcsec (x) y + 2 πn y

Simplify

1 = - arcsec (x) y + 2 πn y

1 = - arcsec (x) y + 2 πn y

Switch sides

- arcsec (x) y + 2 πn y = 1

Factor

- arcsec (x) y + 2 πn y : y (- arcsec (x) + 2 πn)

- arcsec (x) y + 2 πn y

Factor out common term

y

= y (- arcsec (x) + 2 πn)

y (- arcsec (x) + 2 πn) = 1

Divide both sides by

- arcsec (x) + 2 πn

y (- arcsec (x) + 2 πn) = 1

Divide both sides by

- arcsec (x) + 2 πn

\frac{y ( - arcsec ( x ) + 2 πn )}{- arcsec ( x ) + 2 πn} = \frac{1}{- arcsec ( x ) + 2 πn}

Simplify

y = \frac{1}{- arcsec ( x ) + 2 πn}

y = \frac{1}{- arcsec ( x ) + 2 πn}

y = \frac{1}{arcsec ( x ) + 2 πn}, y = \frac{1}{- arcsec ( x ) + 2 πn}

Graph

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sin (x) = \frac{7}{10}

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sin (x) = \frac{7}{11}

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2 sec^{2} (x) = 3 tan (x) + 1

2sec(t)=tan^2(t)+1

2 sec (t) = tan^{2} (t) + 1

sqrt(2)sin(x)-sqrt(2)cos(x)=sqrt(3)

2 sin (x) - 2 cos (x) = 3

Frequently Asked Questions (FAQ)

What is the general solution for solvefor y,x=sec(1/y) ?
The general solution for solvefor y,x=sec(1/y) is y= 1/(arcsec(x)+2pin),y= 1/(-arcsec(x)+2pin)