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Popular >

sqrt(3)= pi/3 sec^2(c)

Solution

3 = \frac{π}{3} sec^{2} (c)

Solution

c = 0.68001 \dots + 2 πn, c = 2 π - 0.68001 \dots + 2 πn, c = 2.46157 \dots + 2 πn, c = - 2.46157 \dots + 2 πn

+1

Degrees

c = 38.96227 \dots^{\circ} + 36 0^{\circ} n, c = 321.03772 \dots^{\circ} + 36 0^{\circ} n, c = 141.03772 \dots^{\circ} + 36 0^{\circ} n, c = - 141.03772 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 = \frac{π}{3} sec^{2} (c)

Switch sides

\frac{π}{3} sec^{2} (c) = 3

Solve by substitution

\frac{π}{3} sec^{2} (c) = 3

Let:

sec (c) = u

\frac{π}{3} u^{2} = 3

\frac{π}{3} u^{2} = 3 : u = \frac{3 3}{π}, u = - \frac{3 3}{π}

\frac{π}{3} u^{2} = 3

Multiply both sides by

3

\frac{π}{3} u^{2} = 3

Multiply both sides by

3

3 \cdot \frac{π}{3} u^{2} = 33

Simplify

π u^{2} = 33

π u^{2} = 33

Divide both sides by

π

π u^{2} = 33

Divide both sides by

π

\frac{π u ^{2}}{π} = \frac{3 3}{π}

Simplify

u^{2} = \frac{3 3}{π}

u^{2} = \frac{3 3}{π}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = \frac{3 3}{π}, u = - \frac{3 3}{π}

Substitute back

u = sec (c)

sec (c) = \frac{3 3}{π}, sec (c) = - \frac{3 3}{π}

sec (c) = \frac{3 3}{π}, sec (c) = - \frac{3 3}{π}

sec (c) = \frac{3 3}{π} : c = arcsec \frac{3 3}{π} + 2 πn, c = 2 π - arcsec \frac{3 3}{π} + 2 πn

sec (c) = \frac{3 3}{π}

Apply trig inverse properties

sec (c) = \frac{3 3}{π}

General solutions for

sec (c) = \frac{3 3}{π}

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

c = arcsec \frac{3 3}{π} + 2 πn, c = 2 π - arcsec \frac{3 3}{π} + 2 πn

c = arcsec \frac{3 3}{π} + 2 πn, c = 2 π - arcsec \frac{3 3}{π} + 2 πn

sec (c) = - \frac{3 3}{π} : c = arcsec - \frac{3 3}{π} + 2 πn, c = - arcsec - \frac{3 3}{π} + 2 πn

sec (c) = - \frac{3 3}{π}

Apply trig inverse properties

sec (c) = - \frac{3 3}{π}

General solutions for

sec (c) = - \frac{3 3}{π}

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

c = arcsec - \frac{3 3}{π} + 2 πn, c = - arcsec - \frac{3 3}{π} + 2 πn

c = arcsec - \frac{3 3}{π} + 2 πn, c = - arcsec - \frac{3 3}{π} + 2 πn

Combine all the solutions

c = arcsec \frac{3 3}{π} + 2 πn, c = 2 π - arcsec \frac{3 3}{π} + 2 πn, c = arcsec - \frac{3 3}{π} + 2 πn, c = - arcsec - \frac{3 3}{π} + 2 πn

Show solutions in decimal form

c = 0.68001 \dots + 2 πn, c = 2 π - 0.68001 \dots + 2 πn, c = 2.46157 \dots + 2 πn, c = - 2.46157 \dots + 2 πn

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