What is the general solution for sin(θ)-cos(θ)=sqrt(3/2),θ[(3pi)/2 ,2pi] ?

The general solution for sin(θ)-cos(θ)=sqrt(3/2),θ[(3pi)/2 ,2pi] is No Solution for θ\in\mathbb{R}

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sin(θ)-cos(θ)=sqrt(3/2),θ[(3pi)/2 ,2pi]

sin (θ) - cos (θ) = \frac{3}{2}, θ [\frac{3 π}{2}, 2 π]

No Solution for θ \in R

Solution steps

sin (θ) - cos (θ) = \frac{3}{2}, θ [\frac{3 π}{2}, 2 π]

Rewrite using trig identities

2 sin (θ - \frac{π}{4}) = \frac{3}{2}

Divide both sides by

2

sin (θ - \frac{π}{4}) = \frac{3}{2}

General solutions for

sin (θ - \frac{π}{4}) = \frac{3}{2}

θ - \frac{π}{4} = \frac{π}{3} + 2 πn, θ - \frac{π}{4} = \frac{2 π}{3} + 2 πn

Solve

θ - \frac{π}{4} = \frac{π}{3} + 2 πn : θ = 2 πn + \frac{7 π}{12}

Solve

θ - \frac{π}{4} = \frac{2 π}{3} + 2 πn : θ = 2 πn + \frac{11 π}{12}

θ = 2 πn + \frac{7 π}{12}, θ = 2 πn + \frac{11 π}{12}

Solutions for the range

θ [\frac{3 π}{2}, 2 π]

No Solution for θ \in R

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tan^{2} (x) - 6 tan (x) - 7 = 0

3 sin (2 x) = 2, 0 \leq x \leq π

cos (θ) = \frac{2}{2.24}

cot (α) = \frac{2}{3}

What is the general solution for sin(θ)-cos(θ)=sqrt(3/2),θ[(3pi)/2 ,2pi] ?
The general solution for sin(θ)-cos(θ)=sqrt(3/2),θ[(3pi)/2 ,2pi] is No Solution for θ\in\mathbb{R}