What is the general solution for sin(((t^2))/2)=-1 ?

The general solution for sin(((t^2))/2)=-1 is t=sqrt(3pi+4pin),t=-sqrt(3pi+4pin)

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sin(((t^2))/2)=-1

sin (\frac{( t ^{2} )}{2}) = - 1

t = 3 π + 4 πn, t = - 3 π + 4 πn

Degrees

t = 0^{\circ} + 268.68695 \dots^{\circ} n, t = 0^{\circ} - 268.68695 \dots^{\circ} n

Solution steps

sin (\frac{( t ^{2} )}{2}) = - 1

General solutions for

sin (\frac{t ^{2}}{2}) = - 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}

\frac{t ^{2}}{2} = \frac{3 π}{2} + 2 πn

\frac{t ^{2}}{2} = \frac{3 π}{2} + 2 πn

Solve

\frac{t ^{2}}{2} = \frac{3 π}{2} + 2 πn : t = 3 π + 4 πn, t = - 3 π + 4 πn

\frac{t ^{2}}{2} = \frac{3 π}{2} + 2 πn

Multiply both sides by

2

\frac{t ^{2}}{2} = \frac{3 π}{2} + 2 πn

Multiply both sides by

2

\frac{2 t ^{2}}{2} = 2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

Simplify

\frac{2 t ^{2}}{2} = 2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

Simplify

\frac{2 t ^{2}}{2} : t^{2}

\frac{2 t ^{2}}{2}

Divide the numbers:

\frac{2}{2} = 1

= t^{2}

Simplify

2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn : 3 π + 4 πn

2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

2 \cdot \frac{3 π}{2} = 3 π

2 \cdot \frac{3 π}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 π 2}{2}

Cancel the common factor:

2

= 3 π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= 3 π + 4 πn

t^{2} = 3 π + 4 πn

t^{2} = 3 π + 4 πn

t^{2} = 3 π + 4 πn

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

t = 3 π + 4 πn, t = - 3 π + 4 πn

t = 3 π + 4 πn, t = - 3 π + 4 πn

9 sin^{2} (x) tan (x) = 4 tan (x)

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

- 2 cos (θ) = 0

2 cos^{2} (x) + 15 sin (x) = 9

cot (θ) = 1.413

What is the general solution for sin(((t^2))/2)=-1 ?
The general solution for sin(((t^2))/2)=-1 is t=sqrt(3pi+4pin),t=-sqrt(3pi+4pin)