What is the general solution for 3sin(2((x-pi)/2))+1=2,5 ?

The general solution for 3sin(2((x-pi)/2))+1=2,5 is No Solution for x\in\mathbb{R}

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3sin(2((x-pi)/2))+1=2,5

3 sin (2 (\frac{x - π}{2})) + 1 = 2, 5

No Solution for x \in R

Solution steps

3 sin (2 (\frac{x - π}{2})) + 1 = 2, 5

Move

1

to the right side

3 sin (2 \frac{x - π}{2}) = 1

Divide both sides by

3

sin (2 \frac{x - π}{2}) = \frac{1}{3}

Apply trig inverse properties

2 \cdot \frac{x - π}{2} = arcsin (\frac{1}{3}) + 2 πn, 2 \cdot \frac{x - π}{2} = π - arcsin (\frac{1}{3}) + 2 πn

Solve

2 \cdot \frac{x - π}{2} = arcsin (\frac{1}{3}) + 2 πn : x = arcsin (\frac{1}{3}) + 2 πn + π

Solve

2 \cdot \frac{x - π}{2} = π - arcsin (\frac{1}{3}) + 2 πn : x = 2 π + 2 πn - arcsin (\frac{1}{3})

x = arcsin (\frac{1}{3}) + 2 πn + π, x = 2 π + 2 πn - arcsin (\frac{1}{3})

Solutions for the range

5

No Solution for x \in R

tan (x) = 0.4627

2 sin^{2} (x) - 4 cos^{2} (x) + 1 = 0

x, - y^{2} - cos (x) = 0

cos (θ) = \frac{6}{16}

∣ cos (x) ∣ = - 1

What is the general solution for 3sin(2((x-pi)/2))+1=2,5 ?
The general solution for 3sin(2((x-pi)/2))+1=2,5 is No Solution for x\in\mathbb{R}