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}

Solution steps

sin (x + \frac{π}{2}) = 0.6

Apply trig inverse properties

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}

Solve

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

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

Show solutions in decimal form

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

4 cot (x) + 1 = 1 + 2 cot (x)

\frac{2}{3} = sin (θ) - 0.28 cos (θ)

2 sin (x) = 3 - cos (x), 0 \leq x \leq 2 π

cos^{2} (x) = - \frac{1}{3}

4 + 4 cos (θ) = 8 cos (θ)

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