What is the general solution for sec(x/2)=2 ?

The general solution for sec(x/2)=2 is x=(2pi)/3+4pin,x=(10pi)/3+4pin

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Popular >

sec(x/2)=2

Solution

sec (\frac{x}{2}) = 2

Solution

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Degrees

x = 12 0^{\circ} + 72 0^{\circ} n, x = 60 0^{\circ} + 72 0^{\circ} n

Solution steps

sec (\frac{x}{2}) = 2

General solutions for

sec (\frac{x}{2}) = 2

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

\frac{x}{2} = \frac{π}{3} + 2 πn, \frac{x}{2} = \frac{5 π}{3} + 2 πn

\frac{x}{2} = \frac{π}{3} + 2 πn, \frac{x}{2} = \frac{5 π}{3} + 2 πn

Solve

\frac{x}{2} = \frac{π}{3} + 2 πn : x = \frac{2 π}{3} + 4 πn

\frac{x}{2} = \frac{π}{3} + 2 πn

Multiply both sides by

2

\frac{x}{2} = \frac{π}{3} + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot \frac{π}{3} + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} = 2 \cdot \frac{π}{3} + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 \cdot \frac{π}{3} + 2 \cdot 2 πn : \frac{2 π}{3} + 4 πn

2 \cdot \frac{π}{3} + 2 \cdot 2 πn

Multiply

2 \cdot \frac{π}{3} : \frac{2 π}{3}

2 \cdot \frac{π}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{3}

= \frac{2 π}{3} + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{5 π}{3} + 2 πn : x = \frac{10 π}{3} + 4 πn

\frac{x}{2} = \frac{5 π}{3} + 2 πn

Multiply both sides by

2

\frac{x}{2} = \frac{5 π}{3} + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot \frac{5 π}{3} + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} = 2 \cdot \frac{5 π}{3} + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 \cdot \frac{5 π}{3} + 2 \cdot 2 πn : \frac{10 π}{3} + 4 πn

2 \cdot \frac{5 π}{3} + 2 \cdot 2 πn

2 \cdot \frac{5 π}{3} = \frac{10 π}{3}

2 \cdot \frac{5 π}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π 2}{3}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Popular Examples

arccos(2x)+arccos(x)= pi/3

arccos (2 x) + arccos (x) = \frac{π}{3}

tan(2x)=(500)/(350-75)

tan (2 x) = \frac{500}{350 - 75}

solvefor y,sin(xy)=x^2 solve for

y, sin (x y) = x^{2}

cos(6x)-cos(x)=0

cos (6 x) - cos (x) = 0

1.74*sin(40.31)=1.33*sin(θ)

1.74 \cdot sin (40.3 1^{\circ}) = 1.33 \cdot sin (θ)

Frequently Asked Questions (FAQ)

What is the general solution for sec(x/2)=2 ?
The general solution for sec(x/2)=2 is x=(2pi)/3+4pin,x=(10pi)/3+4pin