What is the general solution for 7cos(9x)-1=1 ?

The general solution for 7cos(9x)-1=1 is x=(1.28104…)/9+(2pin)/9 ,x=(2pi)/9-(1.28104…)/9+(2pin)/9

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7cos(9x)-1=1

7 cos (9 x) - 1 = 1

x = \frac{1.28104 \dots}{9} + \frac{2 πn}{9}, x = \frac{2 π}{9} - \frac{1.28104 \dots}{9} + \frac{2 πn}{9}

Degrees

x = 8.15538 \dots^{\circ} + 4 0^{\circ} n, x = 31.84461 \dots^{\circ} + 4 0^{\circ} n

Solution steps

7 cos (9 x) - 1 = 1

Move

1

to the right side

7 cos (9 x) - 1 = 1

Add

1

to both sides

7 cos (9 x) - 1 + 1 = 1 + 1

Simplify

7 cos (9 x) = 2

7 cos (9 x) = 2

Divide both sides by

7

7 cos (9 x) = 2

Divide both sides by

7

\frac{7 cos ( 9 x )}{7} = \frac{2}{7}

Simplify

cos (9 x) = \frac{2}{7}

cos (9 x) = \frac{2}{7}

Apply trig inverse properties

cos (9 x) = \frac{2}{7}

General solutions for

cos (9 x) = \frac{2}{7}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

9 x = arccos (\frac{2}{7}) + 2 πn, 9 x = 2 π - arccos (\frac{2}{7}) + 2 πn

9 x = arccos (\frac{2}{7}) + 2 πn, 9 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Solve

9 x = arccos (\frac{2}{7}) + 2 πn : x = \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

9 x = arccos (\frac{2}{7}) + 2 πn

Divide both sides by

9

9 x = arccos (\frac{2}{7}) + 2 πn

Divide both sides by

9

\frac{9 x}{9} = \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

Simplify

x = \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

x = \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

Solve

9 x = 2 π - arccos (\frac{2}{7}) + 2 πn : x = \frac{2 π}{9} - \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

9 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Divide both sides by

9

9 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Divide both sides by

9

\frac{9 x}{9} = \frac{2 π}{9} - \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

Simplify

x = \frac{2 π}{9} - \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

x = \frac{2 π}{9} - \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

x = \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}, x = \frac{2 π}{9} - \frac{arccos ( \frac{2}{7} )}{9} + \frac{2 πn}{9}

Show solutions in decimal form

x = \frac{1.28104 \dots}{9} + \frac{2 πn}{9}, x = \frac{2 π}{9} - \frac{1.28104 \dots}{9} + \frac{2 πn}{9}

cos (22. 5^{\circ})

sin^{2} (x) = \frac{1 - cos ( 2 x )}{2}

sin (- \frac{2 π}{3})

arcsin (- 1)

tan (1)

What is the general solution for 7cos(9x)-1=1 ?
The general solution for 7cos(9x)-1=1 is x=(1.28104…)/9+(2pin)/9 ,x=(2pi)/9-(1.28104…)/9+(2pin)/9