What is the general solution for ((7cos(2x)+7))/2 = pi/2 ?

The general solution for ((7cos(2x)+7))/2 = pi/2 is x=(2.15459…)/2+pin,x=-(2.15459…)/2+pin

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Popular >

((7cos(2x)+7))/2 = pi/2

Solution

\frac{( 7 cos ( 2 x ) + 7 )}{2} = \frac{π}{2}

Solution

x = \frac{2.15459 \dots}{2} + πn, x = - \frac{2.15459 \dots}{2} + πn

Degrees

x = 61.72472 \dots^{\circ} + 18 0^{\circ} n, x = - 61.72472 \dots^{\circ} + 18 0^{\circ} n

Solution steps

\frac{( 7 cos ( 2 x ) + 7 )}{2} = \frac{π}{2}

Multiply both sides by

2

\frac{7 cos ( 2 x ) + 7}{2} = \frac{π}{2}

Multiply both sides by

2

\frac{2 ( 7 cos ( 2 x ) + 7 )}{2} = \frac{2 π}{2}

Simplify

7 cos (2 x) + 7 = π

7 cos (2 x) + 7 = π

Move

7

to the right side

7 cos (2 x) + 7 = π

Subtract

7

from both sides

7 cos (2 x) + 7 - 7 = π - 7

Simplify

7 cos (2 x) = π - 7

7 cos (2 x) = π - 7

Divide both sides by

7

7 cos (2 x) = π - 7

Divide both sides by

7

\frac{7 cos ( 2 x )}{7} = \frac{π}{7} - \frac{7}{7}

Simplify

\frac{7 cos ( 2 x )}{7} = \frac{π}{7} - \frac{7}{7}

Simplify

\frac{7 cos ( 2 x )}{7} : cos (2 x)

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

Divide the numbers:

\frac{7}{7} = 1

= cos (2 x)

Simplify

\frac{π}{7} - \frac{7}{7} : \frac{π - 7}{7}

\frac{π}{7} - \frac{7}{7}

Apply rule

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

= \frac{π - 7}{7}

cos (2 x) = \frac{π - 7}{7}

cos (2 x) = \frac{π - 7}{7}

cos (2 x) = \frac{π - 7}{7}

Apply trig inverse properties

cos (2 x) = \frac{π - 7}{7}

General solutions for

cos (2 x) = \frac{π - 7}{7}

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

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

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

Solve

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

2 x = arccos (\frac{π - 7}{7}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{π - 7}{7}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

Solve

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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{2.15459 \dots}{2} + πn, x = - \frac{2.15459 \dots}{2} + πn

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Frequently Asked Questions (FAQ)

What is the general solution for ((7cos(2x)+7))/2 = pi/2 ?
The general solution for ((7cos(2x)+7))/2 = pi/2 is x=(2.15459…)/2+pin,x=-(2.15459…)/2+pin