What is the general solution for 1=3sin(pi/4 (x-5))+5 ?

The general solution for 1=3sin(pi/4 (x-5))+5 is No Solution for x\in\mathbb{R}

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1=3sin(pi/4 (x-5))+5

1 = 3 sin (\frac{π}{4} (x - 5)) + 5

No Solution for x \in R

Solution steps

1 = 3 sin (\frac{π}{4} (x - 5)) + 5

Switch sides

3 sin (\frac{π}{4} (x - 5)) + 5 = 1

Move

5

to the right side

3 sin (\frac{π}{4} (x - 5)) + 5 = 1

Subtract

5

from both sides

3 sin (\frac{π}{4} (x - 5)) + 5 - 5 = 1 - 5

Simplify

3 sin (\frac{π}{4} (x - 5)) = - 4

3 sin (\frac{π}{4} (x - 5)) = - 4

Divide both sides by

3

3 sin (\frac{π}{4} (x - 5)) = - 4

Divide both sides by

3

\frac{3 sin ( \frac{π}{4} ( x - 5 ) )}{3} = \frac{- 4}{3}

Simplify

sin (\frac{π}{4} (x - 5)) = - \frac{4}{3}

sin (\frac{π}{4} (x - 5)) = - \frac{4}{3}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

sin (x + π) - sin (x) - 1 = 0

4 sin^{2} (x) + 2 sin (x) = 0

tan (x) = 3, - \frac{π}{3} \leq x \leq \frac{3 π}{2}

sin (x) = \frac{5}{16}

sin^{2} (x) + 2 cos (x) = 0

What is the general solution for 1=3sin(pi/4 (x-5))+5 ?
The general solution for 1=3sin(pi/4 (x-5))+5 is No Solution for x\in\mathbb{R}