What is the general solution for 250=100*5*cos(x) ?

The general solution for 250=100*5*cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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250=1005cos(x)

250 = 100 \cdot 5 \cdot cos (x)

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

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

250 = 100 \cdot 5 cos (x)

Switch sides

100 \cdot 5 cos (x) = 250

Divide both sides by

500

100 \cdot 5 cos (x) = 250

Divide both sides by

500

\frac{100 \cdot 5 cos ( x )}{500} = \frac{250}{500}

Simplify

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

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

General solutions for

cos (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}

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

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

What is the general solution for 250=100*5*cos(x) ?
The general solution for 250=100*5*cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin