What is the general solution for sin(θ)=1-cos(θ) ?

The general solution for sin(θ)=1-cos(θ) is θ=2pin,θ=2pin+pi/2

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sin(θ)=1-cos(θ)

sin (θ) = 1 - cos (θ)

θ = 2 πn, θ = 2 πn + \frac{π}{2}

Solution steps

sin (θ) = 1 - cos (θ)

Subtract

1 - cos (θ)

from both sides

sin (θ) - 1 + cos (θ) = 0

Rewrite using trig identities

- 1 + 2 sin (θ + \frac{π}{4}) = 0

Move

1

to the right side

2 sin (θ + \frac{π}{4}) = 1

Divide both sides by

2

sin (θ + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (θ + \frac{π}{4}) = \frac{2}{2}

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

Solve

θ + \frac{π}{4} = \frac{π}{4} + 2 πn : θ = 2 πn

Solve

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

θ = 2 πn, θ = 2 πn + \frac{π}{2}

cos (θ) - 2 sin (θ) cos (θ) = 0

x, cos (x y) = sin (x + y)

cot (x) = \frac{3}{4}

3 sin (x) - cos^{2} (x) + 3 = 0

tan^{2} (x) - 3 = 0, 0 < x < \frac{π}{2}

What is the general solution for sin(θ)=1-cos(θ) ?
The general solution for sin(θ)=1-cos(θ) is θ=2pin,θ=2pin+pi/2