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Popular Trigonometry >

solvefor x,sqrt(3)sec(5x)-2=0

Solution

solvefor

Solution

x = \frac{π}{30} + \frac{2 πn}{5}, x = \frac{11 π}{30} + \frac{2 πn}{5}

+1

Degrees

x = 6^{\circ} + 7 2^{\circ} n, x = 6 6^{\circ} + 7 2^{\circ} n

Solution steps

3 sec (5 x) - 2 = 0

Move

2

to the right side

3 sec (5 x) - 2 = 0

Add

2

to both sides

3 sec (5 x) - 2 + 2 = 0 + 2

Simplify

3 sec (5 x) = 2

3 sec (5 x) = 2

Divide both sides by

3

3 sec (5 x) = 2

Divide both sides by

3

\frac{3 sec ( 5 x )}{3} = \frac{2}{3}

Simplify

\frac{3 sec ( 5 x )}{3} = \frac{2}{3}

Simplify

\frac{3 sec ( 5 x )}{3} : sec (5 x)

\frac{3 sec ( 5 x )}{3}

Cancel the common factor:

3

= sec (5 x)

Simplify

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

sec (5 x) = \frac{2 3}{3}

sec (5 x) = \frac{2 3}{3}

sec (5 x) = \frac{2 3}{3}

General solutions for

sec (5 x) = \frac{2 3}{3}

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}

5 x = \frac{π}{6} + 2 πn, 5 x = \frac{11 π}{6} + 2 πn

5 x = \frac{π}{6} + 2 πn, 5 x = \frac{11 π}{6} + 2 πn

Solve

5 x = \frac{π}{6} + 2 πn : x = \frac{π}{30} + \frac{2 πn}{5}

5 x = \frac{π}{6} + 2 πn

Divide both sides by

5

5 x = \frac{π}{6} + 2 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} = \frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{π}{6}}{5} + \frac{2 πn}{5} : \frac{π}{30} + \frac{2 πn}{5}

\frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{6}}{5} = \frac{π}{30}

\frac{\frac{π}{6}}{5}

Apply the fraction rule:

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

= \frac{π}{6 \cdot 5}

Multiply the numbers:

6 \cdot 5 = 30

= \frac{π}{30}

= \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

Solve

5 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{30} + \frac{2 πn}{5}

5 x = \frac{11 π}{6} + 2 πn

Divide both sides by

5

5 x = \frac{11 π}{6} + 2 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} = \frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5} : \frac{11 π}{30} + \frac{2 πn}{5}

\frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5}

\frac{\frac{11 π}{6}}{5} = \frac{11 π}{30}

\frac{\frac{11 π}{6}}{5}

Apply the fraction rule:

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

= \frac{11 π}{6 \cdot 5}

Multiply the numbers:

6 \cdot 5 = 30

= \frac{11 π}{30}

= \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}, x = \frac{11 π}{30} + \frac{2 πn}{5}

Graph

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