What is the general solution for 7.5=5sin(pi/2 (x-2))+5 ?

The general solution for 7.5=5sin(pi/2 (x-2))+5 is x=4n+7/3 ,x=4n+11/3

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7.5=5sin(pi/2 (x-2))+5

7.5 = 5 sin (\frac{π}{2} (x - 2)) + 5

x = 4 n + \frac{7}{3}, x = 4 n + \frac{11}{3}

Solution steps

7.5 = 5 sin (\frac{π}{2} (x - 2)) + 5

Switch sides

5 sin (\frac{π}{2} (x - 2)) + 5 = 7.5

Move

5

to the right side

5 sin (\frac{π}{2} (x - 2)) = 2.5

Divide both sides by

5

sin (\frac{π}{2} (x - 2)) = 0.5

General solutions for

sin (\frac{π}{2} (x - 2)) = 0.5

\frac{π}{2} (x - 2) = \frac{π}{6} + 2 πn, \frac{π}{2} (x - 2) = \frac{5 π}{6} + 2 πn

Solve

\frac{π}{2} (x - 2) = \frac{π}{6} + 2 πn : x = 4 n + \frac{7}{3}

Solve

\frac{π}{2} (x - 2) = \frac{5 π}{6} + 2 πn : x = 4 n + \frac{11}{3}

x = 4 n + \frac{7}{3}, x = 4 n + \frac{11}{3}

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What is the general solution for 7.5=5sin(pi/2 (x-2))+5 ?
The general solution for 7.5=5sin(pi/2 (x-2))+5 is x=4n+7/3 ,x=4n+11/3