What is the general solution for 500=538cos(x-10) ?

The general solution for 500=538cos(x-10) is x=0.37809…+360n+10,x=360-0.37809…+360n+10

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500=538cos(x-10)

500 = 538 cos (x - 1 0^{\circ})

x = 0.37809 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - 0.37809 \dots + 36 0^{\circ} n + 1 0^{\circ}

Radians

x = 0.37809 \dots + \frac{π}{18} + 2 πn, x = 2 π - 0.37809 \dots + \frac{π}{18} + 2 πn

Solution steps

500 = 538 cos (x - 1 0^{\circ})

Switch sides

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

Divide both sides by

538

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

Divide both sides by

538

\frac{538 cos ( x - 1 0 ^{\circ} )}{538} = \frac{500}{538}

Simplify

cos (x - 1 0^{\circ}) = \frac{250}{269}

cos (x - 1 0^{\circ}) = \frac{250}{269}

Apply trig inverse properties

cos (x - 1 0^{\circ}) = \frac{250}{269}

General solutions for

cos (x - 1 0^{\circ}) = \frac{250}{269}

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{250}{269}) + 36 0^{\circ} n, x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n

x - 1 0^{\circ} = arccos (\frac{250}{269}) + 36 0^{\circ} n, x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n

Solve

x - 1 0^{\circ} = arccos (\frac{250}{269}) + 36 0^{\circ} n : x = arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = arccos (\frac{250}{269}) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x - 1 0^{\circ} = arccos (\frac{250}{269}) + 36 0^{\circ} n

Add

1 0^{\circ}

to both sides

x - 1 0^{\circ} + 1 0^{\circ} = arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

Simplify

x = arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

x = arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

Solve

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n

Add

1 0^{\circ}

to both sides

x - 1 0^{\circ} + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

Simplify

x = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

x = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

x = arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{250}{269}) + 36 0^{\circ} n + 1 0^{\circ}

Show solutions in decimal form

x = 0.37809 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 36 0^{\circ} - 0.37809 \dots + 36 0^{\circ} n + 1 0^{\circ}

0 = sec^{2} (x) e^{t a n (x)} (2 tan (x) + sec^{2} (x))

tan (x) = 3, - 18 0^{\circ} < x < 18 0^{\circ}

cot^{2} (t) csc (t) = sin (t)

\frac{6}{12} = cos (θ)

sin (a) = \frac{6.88}{6.9}

What is the general solution for 500=538cos(x-10) ?
The general solution for 500=538cos(x-10) is x=0.37809…+360n+10,x=360-0.37809…+360n+10