What is the general solution for solvefor y,-1/2 cot(y)=(t^2)/2+C ?

The general solution for solvefor y,-1/2 cot(y)=(t^2)/2+C is y=arccot(-t^2-2C)+pin

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solvefor y,-1/2 cot(y)=(t^2)/2+C

solve for

y, - \frac{1}{2} cot (y) = \frac{t ^{2}}{2} + C

y = arccot (- t^{2} - 2 C) + πn

Solution steps

- \frac{1}{2} cot (y) = \frac{t ^{2}}{2} + C

Multiply both sides by

- 2

- \frac{1}{2} cot (y) = \frac{t ^{2}}{2} + C

Multiply both sides by

- 2

(- \frac{1}{2} cot (y)) (- 2) = \frac{t ^{2}}{2} (- 2) + C (- 2)

Simplify

(- \frac{1}{2} cot (y)) (- 2) = \frac{t ^{2}}{2} (- 2) + C (- 2)

Simplify

(- \frac{1}{2} cot (y)) (- 2) : cot (y)

(- \frac{1}{2} cot (y)) (- 2)

Remove parentheses:

(- a) = - a, - (- a) = a

= \frac{1}{2} cot (y) \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2} cot (y)

Cancel the common factor:

2

= cot (y) \cdot 1

Multiply:

cot (y) \cdot 1 = cot (y)

= cot (y)

Simplify

\frac{t ^{2}}{2} (- 2) + C (- 2) : - t^{2} - 2 C

\frac{t ^{2}}{2} (- 2) + C (- 2)

Remove parentheses:

(- a) = - a

= - \frac{t ^{2}}{2} \cdot 2 - C \cdot 2

\frac{t ^{2}}{2} \cdot 2 = t^{2}

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

Multiply fractions:

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

= \frac{t ^{2} \cdot 2}{2}

Cancel the common factor:

2

= t^{2}

= - t^{2} - 2 C

cot (y) = - t^{2} - 2 C

cot (y) = - t^{2} - 2 C

cot (y) = - t^{2} - 2 C

Apply trig inverse properties

cot (y) = - t^{2} - 2 C

General solutions for

cot (y) = - t^{2} - 2 C

cot (x) = a \Rightarrow x = arccot (a) + πn

y = arccot (- t^{2} - 2 C) + πn

y = arccot (- t^{2} - 2 C) + πn

4 cos (2 t) + 1 = 3, 0, \frac{π}{2}

A, cos (\frac{π}{3} - A) = 2 sin (A)

- 3 + 3 = 26 cos (θ)

sin (\frac{π}{2} - x) = - 1, 0^{\circ} \leq x \leq 36 0^{\circ}

2 sin (5 x) = - 1

What is the general solution for solvefor y,-1/2 cot(y)=(t^2)/2+C ?
The general solution for solvefor y,-1/2 cot(y)=(t^2)/2+C is y=arccot(-t^2-2C)+pin