What is the general solution for sin(x+pi/2)=0.6 ?

The general solution for sin(x+pi/2)=0.6 is x=0.64350…+2pin-pi/2 ,x=pi-0.64350…+2pin-pi/2

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sin(x+pi/2)=0.6

sin (x + \frac{π}{2}) = 0.6

x = 0.64350 \dots + 2 πn - \frac{π}{2}, x = π - 0.64350 \dots + 2 πn - \frac{π}{2}

Degrees

x = - 53.13010 \dots^{\circ} + 36 0^{\circ} n, x = 53.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x + \frac{π}{2}) = 0.6

Apply trig inverse properties

sin (x + \frac{π}{2}) = 0.6

General solutions for

sin (x + \frac{π}{2}) = 0.6

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x + \frac{π}{2} = arcsin (0.6) + 2 πn, x + \frac{π}{2} = π - arcsin (0.6) + 2 πn

x + \frac{π}{2} = arcsin (0.6) + 2 πn, x + \frac{π}{2} = π - arcsin (0.6) + 2 πn

Solve

x + \frac{π}{2} = arcsin (0.6) + 2 πn : x = arcsin (0.6) + 2 πn - \frac{π}{2}

x + \frac{π}{2} = arcsin (0.6) + 2 πn

Move

\frac{π}{2}

to the right side

x + \frac{π}{2} = arcsin (0.6) + 2 πn

Subtract

\frac{π}{2}

from both sides

x + \frac{π}{2} - \frac{π}{2} = arcsin (0.6) + 2 πn - \frac{π}{2}

Simplify

x = arcsin (0.6) + 2 πn - \frac{π}{2}

x = arcsin (0.6) + 2 πn - \frac{π}{2}