What is the general solution for 81pi=10.5-9cos(pi/(30)t) ?

The general solution for 81pi=10.5-9cos(pi/(30)t) is No Solution for t\in\mathbb{R}

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81pi=10.5-9cos(pi/(30)t)

81 π = 10.5 - 9 cos (\frac{π}{30} t)

No Solution for t \in R

Solution steps

81 π = 10.5 - 9 cos (\frac{π}{30} t)

Switch sides

10.5 - 9 cos (\frac{π}{30} t) = 81 π

Move

10.5

to the right side

10.5 - 9 cos (\frac{π}{30} t) = 81 π

Subtract

10.5

from both sides

10.5 - 9 cos (\frac{π}{30} t) - 10.5 = 81 π - 10.5

Simplify

- 9 cos (\frac{π}{30} t) = 243.96900 \dots

- 9 cos (\frac{π}{30} t) = 243.96900 \dots

Divide both sides by

- 9

- 9 cos (\frac{π}{30} t) = 243.96900 \dots

Divide both sides by

- 9

\frac{- 9 cos ( \frac{π}{30} t )}{- 9} = \frac{243.96900 \dots}{- 9}

Simplify

\frac{- 9 cos ( \frac{π}{30} t )}{- 9} = \frac{243.96900 \dots}{- 9}

Simplify

\frac{- 9 cos ( \frac{π}{30} t )}{- 9} : cos (\frac{π}{30} t)

\frac{- 9 cos ( \frac{π}{30} t )}{- 9}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{9 cos ( \frac{π}{30} t )}{9}

Divide the numbers:

\frac{9}{9} = 1

= cos (\frac{π}{30} t)

Simplify

\frac{243.96900 \dots}{- 9} : - 27.10766 \dots

\frac{243.96900 \dots}{- 9}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{243.96900 \dots}{9}

Divide the numbers:

\frac{243.96900 \dots}{9} = 27.10766 \dots

= - 27.10766 \dots

cos (\frac{π}{30} t) = - 27.10766 \dots

cos (\frac{π}{30} t) = - 27.10766 \dots

cos (\frac{π}{30} t) = - 27.10766 \dots

- 1 \leq cos (x) \leq 1

No Solution for t \in R

5 - 9 cos (x) = 0

tan^{2} (x) = 500

cot (x) + tan (x) = 1

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

tan (x) = 2 - cot (x)

What is the general solution for 81pi=10.5-9cos(pi/(30)t) ?
The general solution for 81pi=10.5-9cos(pi/(30)t) is No Solution for t\in\mathbb{R}