What is the general solution for 16cos(8x)-2=6 ?

The general solution for 16cos(8x)-2=6 is x= pi/(24)+(pin)/4 ,x=(5pi}{24}+\frac{pin)/4

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Popular >

16cos(8x)-2=6

Solution

16 cos (8 x) - 2 = 6

Solution

x = \frac{π}{24} + \frac{πn}{4}, x = \frac{5 π}{24} + \frac{πn}{4}

Degrees

x = 7. 5^{\circ} + 4 5^{\circ} n, x = 37. 5^{\circ} + 4 5^{\circ} n

Solution steps

16 cos (8 x) - 2 = 6

Move

2

to the right side

16 cos (8 x) - 2 = 6

Add

2

to both sides

16 cos (8 x) - 2 + 2 = 6 + 2

Simplify

16 cos (8 x) = 8

16 cos (8 x) = 8

Divide both sides by

16

16 cos (8 x) = 8

Divide both sides by

16

\frac{16 cos ( 8 x )}{16} = \frac{8}{16}

Simplify

cos (8 x) = \frac{1}{2}

cos (8 x) = \frac{1}{2}

General solutions for

cos (8 x) = \frac{1}{2}

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

8 x = \frac{π}{3} + 2 πn, 8 x = \frac{5 π}{3} + 2 πn

8 x = \frac{π}{3} + 2 πn, 8 x = \frac{5 π}{3} + 2 πn

Solve

8 x = \frac{π}{3} + 2 πn : x = \frac{π}{24} + \frac{πn}{4}

8 x = \frac{π}{3} + 2 πn

Divide both sides by

8

8 x = \frac{π}{3} + 2 πn

Divide both sides by

8

\frac{8 x}{8} = \frac{\frac{π}{3}}{8} + \frac{2 πn}{8}

Simplify

\frac{8 x}{8} = \frac{\frac{π}{3}}{8} + \frac{2 πn}{8}

Simplify

\frac{8 x}{8} : x

\frac{8 x}{8}

Divide the numbers:

\frac{8}{8} = 1

= x

Simplify

\frac{\frac{π}{3}}{8} + \frac{2 πn}{8} : \frac{π}{24} + \frac{πn}{4}

\frac{\frac{π}{3}}{8} + \frac{2 πn}{8}

\frac{\frac{π}{3}}{8} = \frac{π}{24}

\frac{\frac{π}{3}}{8}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 8}

Multiply the numbers:

3 \cdot 8 = 24

= \frac{π}{24}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

Cancel the common factor:

2

= \frac{πn}{4}

= \frac{π}{24} + \frac{πn}{4}

x = \frac{π}{24} + \frac{πn}{4}

x = \frac{π}{24} + \frac{πn}{4}

x = \frac{π}{24} + \frac{πn}{4}

Solve

8 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{24} + \frac{πn}{4}

8 x = \frac{5 π}{3} + 2 πn

Divide both sides by

8

8 x = \frac{5 π}{3} + 2 πn

Divide both sides by

8

\frac{8 x}{8} = \frac{\frac{5 π}{3}}{8} + \frac{2 πn}{8}

Simplify

\frac{8 x}{8} = \frac{\frac{5 π}{3}}{8} + \frac{2 πn}{8}

Simplify

\frac{8 x}{8} : x

\frac{8 x}{8}

Divide the numbers:

\frac{8}{8} = 1

= x

Simplify

\frac{\frac{5 π}{3}}{8} + \frac{2 πn}{8} : \frac{5 π}{24} + \frac{πn}{4}

\frac{\frac{5 π}{3}}{8} + \frac{2 πn}{8}

\frac{\frac{5 π}{3}}{8} = \frac{5 π}{24}

\frac{\frac{5 π}{3}}{8}

Apply the fraction rule:

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

= \frac{5 π}{3 \cdot 8}

Multiply the numbers:

3 \cdot 8 = 24

= \frac{5 π}{24}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

Cancel the common factor:

2

= \frac{πn}{4}

= \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{π}{24} + \frac{πn}{4}, x = \frac{5 π}{24} + \frac{πn}{4}

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Frequently Asked Questions (FAQ)

What is the general solution for 16cos(8x)-2=6 ?
The general solution for 16cos(8x)-2=6 is x= pi/(24)+(pin)/4 ,x=(5pi}{24}+\frac{pin)/4