What is the general solution for sin(X)=1 ?

The general solution for sin(X)=1 is X= pi/2+2pin

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sin(X)=1

sin (X) = 1

X = \frac{π}{2} + 2 πn

Degrees

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

Solution steps

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

x, \frac{17}{sin ( x )} = \frac{23}{sin ( 7 5 ^{\circ} )}

3 - 2 cos^{2} (x) = 4 sin^{2} (x)

4 - 4 cos (2 x) - 3 sin (x) = 0

2 sin^{2} (w) + sin (w) - 1 = 0

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

What is the general solution for sin(X)=1 ?
The general solution for sin(X)=1 is X= pi/2+2pin