What is the general solution for 0=3sin(x+pi/2) ?

The general solution for 0=3sin(x+pi/2) is x=2pin-pi/2 ,x=pi+2pin-pi/2

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0=3sin(x+pi/2)

0 = 3 sin (x + \frac{π}{2})

x = 2 πn - \frac{π}{2}, x = π + 2 πn - \frac{π}{2}

Degrees

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

Solution steps

0 = 3 sin (x + \frac{π}{2})

Switch sides

3 sin (x + \frac{π}{2}) = 0

Divide both sides by

3

3 sin (x + \frac{π}{2}) = 0

Divide both sides by

3

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

Simplify

sin (x + \frac{π}{2}) = 0

sin (x + \frac{π}{2}) = 0

General solutions for

sin (x + \frac{π}{2}) = 0

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} = 0 + 2 πn, x + \frac{π}{2} = π + 2 πn

x + \frac{π}{2} = 0 + 2 πn, x + \frac{π}{2} = π + 2 πn

Solve

x + \frac{π}{2} = 0 + 2 πn : x = 2 πn - \frac{π}{2}

x + \frac{π}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

x + \frac{π}{2} = 2 πn

Move

\frac{π}{2}

to the right side

x + \frac{π}{2} = 2 πn

Subtract

\frac{π}{2}

from both sides

x + \frac{π}{2} - \frac{π}{2} = 2 πn - \frac{π}{2}

Simplify

x = 2 πn - \frac{π}{2}

x = 2 πn - \frac{π}{2}

Solve

x + \frac{π}{2} = π + 2 πn : x = π + 2 πn - \frac{π}{2}

x + \frac{π}{2} = π + 2 πn

Move

\frac{π}{2}

to the right side

x + \frac{π}{2} = π + 2 πn

Subtract

\frac{π}{2}

from both sides

x + \frac{π}{2} - \frac{π}{2} = π + 2 πn - \frac{π}{2}

Simplify

x = π + 2 πn - \frac{π}{2}

x = π + 2 πn - \frac{π}{2}

x = 2 πn - \frac{π}{2}, x = π + 2 πn - \frac{π}{2}

- cos (t) = cos (t)

sin^{2} (x) - cos (2 x) = - \frac{1}{4}

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

- 5 π sin (\frac{π ( t )}{2}) = 7.071

9.8 \cdot sin (x) - 19.6 \cdot cos (x) = 4.7

What is the general solution for 0=3sin(x+pi/2) ?
The general solution for 0=3sin(x+pi/2) is x=2pin-pi/2 ,x=pi+2pin-pi/2