What is the general solution for 5sin((2x-pi)/2)=0.5 ?

The general solution for 5sin((2x-pi)/2)=0.5 is x= pi/2+2pin+0.10016…,x=(3pi)/2+2pin-0.10016…

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5sin((2x-pi)/2)=0.5

5 sin (\frac{2 x - π}{2}) = 0.5

x = \frac{π}{2} + 2 πn + 0.10016 \dots, x = \frac{3 π}{2} + 2 πn - 0.10016 \dots

Solution steps

5 sin (\frac{2 x - π}{2}) = 0.5

Divide both sides by

5

sin (\frac{2 x - π}{2}) = 0.1

Apply trig inverse properties

\frac{2 x - π}{2} = arcsin (0.1) + 2 πn, \frac{2 x - π}{2} = π - arcsin (0.1) + 2 πn

Solve

\frac{2 x - π}{2} = arcsin (0.1) + 2 πn : x = \frac{π}{2} + 2 πn + arcsin (0.1)

Solve

\frac{2 x - π}{2} = π - arcsin (0.1) + 2 πn : x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

x = \frac{π}{2} + 2 πn + arcsin (0.1), x = \frac{3 π}{2} + 2 πn - arcsin (0.1)

Show solutions in decimal form

x = \frac{π}{2} + 2 πn + 0.10016 \dots, x = \frac{3 π}{2} + 2 πn - 0.10016 \dots

16 sin^{2} (θ) = 12

tan (θ) = - \frac{57}{9}

sin^{2} (x) = \frac{2}{3}

sin (4 y) + sin (6 y) + cos (y) = 0

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

What is the general solution for 5sin((2x-pi)/2)=0.5 ?
The general solution for 5sin((2x-pi)/2)=0.5 is x= pi/2+2pin+0.10016…,x=(3pi)/2+2pin-0.10016…