What is the general solution for 75= 120/4*cos((2*pi*x)/(360))+120/2 ?

The general solution for 75= 120/4*cos((2*pi*x)/(360))+120/2 is x=60+360n,x=300+360n

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75= 120/4cos((2pi*x)/(360))+120/2

75 = \frac{120}{4} \cdot cos (\frac{2 \cdot π \cdot x}{360}) + \frac{120}{2}

x = 60 + 360 n, x = 300 + 360 n

Solution steps

75 = \frac{120}{4} cos (\frac{2 π x}{360}) + \frac{120}{2}

Switch sides

\frac{120}{4} cos (\frac{2 π x}{360}) + \frac{120}{2} = 75

\frac{120}{4} cos (\frac{2 π x}{360}) = 30 cos (\frac{2 π x}{360})

\frac{120}{2} = 60

30 cos (\frac{2 π x}{360}) + 60 = 75

Move

60

to the right side

30 cos (\frac{2 π x}{360}) = 15

Divide both sides by

30

cos (\frac{2 π x}{360}) = \frac{1}{2}

General solutions for

cos (\frac{2 π x}{360}) = \frac{1}{2}

\frac{2 π x}{360} = \frac{π}{3} + 2 πn, \frac{2 π x}{360} = \frac{5 π}{3} + 2 πn

Solve

\frac{2 π x}{360} = \frac{π}{3} + 2 πn : x = 60 + 360 n

Solve

\frac{2 π x}{360} = \frac{5 π}{3} + 2 πn : x = 300 + 360 n

x = 60 + 360 n, x = 300 + 360 n

cot^{2} (x) + 2 = 2 csc (x)

3 sin (x) + cos (x) = 2

15 cos^{2} (x) - 4 cos (x) - 3 = 0

- 3 sin^{2} (θ) + 3 = - cos (θ) + 2

tan^{2} (x) - 4 sec (x) + 5 = 0

What is the general solution for 75= 120/4*cos((2*pi*x)/(360))+120/2 ?
The general solution for 75= 120/4*cos((2*pi*x)/(360))+120/2 is x=60+360n,x=300+360n