What is the general solution for solvefor c,e=r(sec(c/2)-1) ?

The general solution for solvefor c,e=r(sec(c/2)-1) is c=2arcsec(e/r+1)+4pin,c=-2arcsec(e/r+1)+4pin

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solvefor c,e=r(sec(c/2)-1)

Solution

solve for

c, e = r (sec (\frac{c}{2}) - 1)

Solution

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn, c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

Solution steps

e = r (sec (\frac{c}{2}) - 1)

Switch sides

r (sec (\frac{c}{2}) - 1) = e

Divide both sides by

r; r \neq = 0

r (sec (\frac{c}{2}) - 1) = e

Divide both sides by

r; r \neq = 0

\frac{r ( sec ( \frac{c}{2} ) - 1 )}{r} = \frac{e}{r}; r \neq = 0

Simplify

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

Move

1

to the right side

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

Add

1

to both sides

sec (\frac{c}{2}) - 1 + 1 = \frac{e}{r} + 1; r \neq = 0

Simplify

sec (\frac{c}{2}) = \frac{e}{r} + 1; r \neq = 0

sec (\frac{c}{2}) = \frac{e}{r} + 1; r \neq = 0

Apply trig inverse properties

sec (\frac{c}{2}) = \frac{e}{r} + 1

General solutions for

sec (\frac{c}{2}) = \frac{e}{r} + 1

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

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn, \frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn, \frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

Solve

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn : c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

Multiply both sides by

2

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

Multiply both sides by

2

\frac{2 c}{2} = 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Simplify

\frac{2 c}{2} = 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Simplify

\frac{2 c}{2} : c

\frac{2 c}{2}

Divide the numbers:

\frac{2}{2} = 1

= c

Simplify

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn : 2 arcsec (\frac{e}{r} + 1) + 4 πn

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

Solve

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn : c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

Multiply both sides by

2

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

Multiply both sides by

2

\frac{2 c}{2} = - 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Simplify

\frac{2 c}{2} = - 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Simplify

\frac{2 c}{2} : c

\frac{2 c}{2}

Divide the numbers:

\frac{2}{2} = 1

= c

Simplify

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn : - 2 arcsec (\frac{e}{r} + 1) + 4 πn

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn, c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor c,e=r(sec(c/2)-1) ?
The general solution for solvefor c,e=r(sec(c/2)-1) is c=2arcsec(e/r+1)+4pin,c=-2arcsec(e/r+1)+4pin