What is the general solution for solvefor x,sin(x)-1=0 ?

The general solution for solvefor x,sin(x)-1=0 is x= pi/2+2pin

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solvefor x,sin(x)-1=0

solve for

x, sin (x) - 1 = 0

x = \frac{π}{2} + 2 πn

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) - 1 = 0

Move

1

to the right side

sin (x) - 1 = 0

Add

1

to both sides

sin (x) - 1 + 1 = 0 + 1

Simplify

sin (x) = 1

sin (x) = 1

General solutions for

sin (x) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

sin^{2} (θ) = 1 + cos (2 θ)

4 sin^{2} (θ) = 3 - 2 sin^{2} (θ)

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

sin (2 θ) = 0.5

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

What is the general solution for solvefor x,sin(x)-1=0 ?
The general solution for solvefor x,sin(x)-1=0 is x= pi/2+2pin