What is the general solution for 500=538.5cos(x-10) ?

The general solution for 500=538.5cos(x-10) is x=0.38042…+360n+10,x=360-0.38042…+360n+10

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Popular >

500=538.5cos(x-10)

Solution

500 = 538.5 cos (x - 1 0^{\circ})

Solution

x = 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}

Radians

x = 0.38042 \dots + \frac{π}{18} + 2 πn, x = 2 π - 0.38042 \dots + \frac{π}{18} + 2 πn

Solution steps

500 = 538.5 cos (x - 1 0^{\circ})

Switch sides

538.5 cos (x - 1 0^{\circ}) = 500

Multiply both sides by

10

538.5 cos (x - 1 0^{\circ}) = 500

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

538.5 cos (x - 1 0^{\circ}) \cdot 10 = 500 \cdot 10

Refine

5385 cos (x - 1 0^{\circ}) = 5000

5385 cos (x - 1 0^{\circ}) = 5000

Divide both sides by

5385

5385 cos (x - 1 0^{\circ}) = 5000

Divide both sides by

5385

\frac{5385 cos ( x - 1 0 ^{\circ} )}{5385} = \frac{5000}{5385}

Simplify

cos (x - 1 0^{\circ}) = \frac{1000}{1077}

cos (x - 1 0^{\circ}) = \frac{1000}{1077}

Apply trig inverse properties

cos (x - 1 0^{\circ}) = \frac{1000}{1077}

General solutions for

cos (x - 1 0^{\circ}) = \frac{1000}{1077}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n, x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n, x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

Solve

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n : x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x - 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n

Add

1 0^{\circ}

to both sides

x - 1 0^{\circ} + 1 0^{\circ} = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

Simplify

x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

Solve

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n

Add

1 0^{\circ}

to both sides

x - 1 0^{\circ} + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

Simplify

x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

x = arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{1000}{1077}) + 36 0^{\circ} n + 1 0^{\circ}

Show solutions in decimal form

x = 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - 0.38042 \dots + 36 0^{\circ} n + 1 0^{\circ}

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Frequently Asked Questions (FAQ)

What is the general solution for 500=538.5cos(x-10) ?
The general solution for 500=538.5cos(x-10) is x=0.38042…+360n+10,x=360-0.38042…+360n+10