What is the general solution for sin(x+pi/4)=\pm 1 ?

The general solution for sin(x+pi/4)=\pm 1 is No Solution for x\in\mathbb{R}

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sin(x+pi/4)=\pm 1

sin (x + \frac{π}{4}) = \pm 1

No Solution for x \in R

Solution steps

sin (x + \frac{π}{4}) = \pm 1

Apply trig inverse properties

sin (x + \frac{π}{4}) = \pm 1

General solutions for

sin (x + \frac{π}{4}) = \pm 1

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

x + \frac{π}{4} = arcsin (\pm 1) + 2 πn, x + \frac{π}{4} = π + arcsin (- \pm 1) + 2 πn

x + \frac{π}{4} = arcsin (\pm 1) + 2 πn, x + \frac{π}{4} = π + arcsin (- \pm 1) + 2 πn

Solve

x + \frac{π}{4} = arcsin (\pm 1) + 2 πn : x = arcsin (\pm 1) + 2 πn - \frac{π}{4}

x + \frac{π}{4} = arcsin (\pm 1) + 2 πn

Move

\frac{π}{4}

to the right side

x + \frac{π}{4} = arcsin (\pm 1) + 2 πn

Subtract

\frac{π}{4}

from both sides

x + \frac{π}{4} - \frac{π}{4} = arcsin (\pm 1) + 2 πn - \frac{π}{4}

Simplify

x = arcsin (\pm 1) + 2 πn - \frac{π}{4}

x = arcsin (\pm 1) + 2 πn - \frac{π}{4}