What is the general solution for solvefor y,(sqrt(3))/2 =sin(arcsin(0)+y) ?

The general solution for solvefor y,(sqrt(3))/2 =sin(arcsin(0)+y) is y= pi/3+2pin,y=(2pi)/3+2pin

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solvefor y,(sqrt(3))/2 =sin(arcsin(0)+y)

solve for

y, \frac{3}{2} = sin (arcsin (0) + y)

y = \frac{π}{3} + 2 πn, y = \frac{2 π}{3} + 2 πn

Solution steps

\frac{3}{2} = sin (arcsin (0) + y)

Switch sides

sin (arcsin (0) + y) = \frac{3}{2}

arcsin (0) = 0

arcsin (0)

Use the following trivial identity:

arcsin (0) = 0

arcsin (0)

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= 0

= 0

sin (0 + y) = \frac{3}{2}

General solutions for

sin (0 + y) = \frac{3}{2}

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}

0 + y = \frac{π}{3} + 2 πn, 0 + y = \frac{2 π}{3} + 2 πn

0 + y = \frac{π}{3} + 2 πn, 0 + y = \frac{2 π}{3} + 2 πn

Solve

0 + y = \frac{π}{3} + 2 πn : y = \frac{π}{3} + 2 πn

0 + y = \frac{π}{3} + 2 πn

0 + y = y

y = \frac{π}{3} + 2 πn

Solve

0 + y = \frac{2 π}{3} + 2 πn : y = \frac{2 π}{3} + 2 πn

0 + y = \frac{2 π}{3} + 2 πn

0 + y = y

y = \frac{2 π}{3} + 2 πn

y = \frac{π}{3} + 2 πn, y = \frac{2 π}{3} + 2 πn

2 \cdot cos^{2} (x) - cos (x) - 1 = 0

tan^{2} (x) - cot (x) = 0

5 sec^{3} (x) - 20 sec (x) = 0

3 cot^{2} (x) - 1 = 0, x

cos^{2} (x) + cos (2 x) = 0

What is the general solution for solvefor y,(sqrt(3))/2 =sin(arcsin(0)+y) ?
The general solution for solvefor y,(sqrt(3))/2 =sin(arcsin(0)+y) is y= pi/3+2pin,y=(2pi)/3+2pin