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Popular >

90+45cos((t^2)/(18))-100=0

Solution

90 + 45 cos (\frac{t ^{2}}{18}) - 100 = 0

Solution

t = 18 \cdot 1.34670 \dots + 36 πn, t = - 18 \cdot 1.34670 \dots + 36 πn, t = 36 π - 18 \cdot 1.34670 \dots + 36 πn, t = - 36 π - 18 \cdot 1.34670 \dots + 36 πn

Degrees

t = 0^{\circ} + 671.45665 \dots^{\circ} n, t = 0^{\circ} - 671.45665 \dots^{\circ} n, t = 0^{\circ} + 814.23333 \dots^{\circ} n, t = 0^{\circ} - 814.23333 \dots^{\circ} n

Solution steps

90 + 45 cos (\frac{t ^{2}}{18}) - 100 = 0

Group like terms

45 cos (\frac{t ^{2}}{18}) + 90 - 100 = 0

Add/Subtract the numbers:

90 - 100 = - 10

45 cos (\frac{t ^{2}}{18}) - 10 = 0

Move

10

to the right side

45 cos (\frac{t ^{2}}{18}) - 10 = 0

Add

10

to both sides

45 cos (\frac{t ^{2}}{18}) - 10 + 10 = 0 + 10

Simplify

45 cos (\frac{t ^{2}}{18}) = 10

45 cos (\frac{t ^{2}}{18}) = 10

Divide both sides by

45

45 cos (\frac{t ^{2}}{18}) = 10

Divide both sides by

45

\frac{45 cos ( \frac{t ^{2}}{18} )}{45} = \frac{10}{45}

Simplify

cos (\frac{t ^{2}}{18}) = \frac{2}{9}

cos (\frac{t ^{2}}{18}) = \frac{2}{9}

Apply trig inverse properties

cos (\frac{t ^{2}}{18}) = \frac{2}{9}

General solutions for

cos (\frac{t ^{2}}{18}) = \frac{2}{9}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

\frac{t ^{2}}{18} = arccos (\frac{2}{9}) + 2 πn, \frac{t ^{2}}{18} = 2 π - arccos (\frac{2}{9}) + 2 πn

\frac{t ^{2}}{18} = arccos (\frac{2}{9}) + 2 πn, \frac{t ^{2}}{18} = 2 π - arccos (\frac{2}{9}) + 2 πn

Solve

\frac{t ^{2}}{18} = arccos (\frac{2}{9}) + 2 πn : t = 18 arccos (\frac{2}{9}) + 36 πn, t = - 18 arccos (\frac{2}{9}) + 36 πn

\frac{t ^{2}}{18} = arccos (\frac{2}{9}) + 2 πn

Multiply both sides by

18

\frac{t ^{2}}{18} = arccos (\frac{2}{9}) + 2 πn

Multiply both sides by

18

\frac{18 t ^{2}}{18} = 18 arccos (\frac{2}{9}) + 18 \cdot 2 πn

Simplify

\frac{18 t ^{2}}{18} = 18 arccos (\frac{2}{9}) + 18 \cdot 2 πn

Simplify

\frac{18 t ^{2}}{18} : t^{2}

\frac{18 t ^{2}}{18}

Divide the numbers:

\frac{18}{18} = 1

= t^{2}

Simplify

18 arccos (\frac{2}{9}) + 18 \cdot 2 πn : 18 arccos (\frac{2}{9}) + 36 πn

18 arccos (\frac{2}{9}) + 18 \cdot 2 πn

Multiply the numbers:

18 \cdot 2 = 36

= 18 arccos (\frac{2}{9}) + 36 πn

t^{2} = 18 arccos (\frac{2}{9}) + 36 πn

t^{2} = 18 arccos (\frac{2}{9}) + 36 πn

t^{2} = 18 arccos (\frac{2}{9}) + 36 πn

For

x^{2} = f (a)

the solutions are

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

t = 18 arccos (\frac{2}{9}) + 36 πn, t = - 18 arccos (\frac{2}{9}) + 36 πn

Solve

\frac{t ^{2}}{18} = 2 π - arccos (\frac{2}{9}) + 2 πn : t = 36 π - 18 arccos (\frac{2}{9}) + 36 πn, t = - 36 π - 18 arccos (\frac{2}{9}) + 36 πn

\frac{t ^{2}}{18} = 2 π - arccos (\frac{2}{9}) + 2 πn

Multiply both sides by

18

\frac{t ^{2}}{18} = 2 π - arccos (\frac{2}{9}) + 2 πn

Multiply both sides by

18

\frac{18 t ^{2}}{18} = 18 \cdot 2 π - 18 arccos (\frac{2}{9}) + 18 \cdot 2 πn

Simplify

\frac{18 t ^{2}}{18} = 18 \cdot 2 π - 18 arccos (\frac{2}{9}) + 18 \cdot 2 πn

Simplify

\frac{18 t ^{2}}{18} : t^{2}

\frac{18 t ^{2}}{18}

Divide the numbers:

\frac{18}{18} = 1

= t^{2}

Simplify

18 \cdot 2 π - 18 arccos (\frac{2}{9}) + 18 \cdot 2 πn : 36 π - 18 arccos (\frac{2}{9}) + 36 πn

18 \cdot 2 π - 18 arccos (\frac{2}{9}) + 18 \cdot 2 πn

Multiply the numbers:

18 \cdot 2 = 36

= 36 π - 18 arccos (\frac{2}{9}) + 36 πn

t^{2} = 36 π - 18 arccos (\frac{2}{9}) + 36 πn

t^{2} = 36 π - 18 arccos (\frac{2}{9}) + 36 πn

t^{2} = 36 π - 18 arccos (\frac{2}{9}) + 36 πn

For

x^{2} = f (a)

the solutions are

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

t = 36 π - 18 arccos (\frac{2}{9}) + 36 πn, t = - 36 π - 18 arccos (\frac{2}{9}) + 36 πn

t = 18 arccos (\frac{2}{9}) + 36 πn, t = - 18 arccos (\frac{2}{9}) + 36 πn, t = 36 π - 18 arccos (\frac{2}{9}) + 36 πn, t = - 36 π - 18 arccos (\frac{2}{9}) + 36 πn

Show solutions in decimal form

t = 18 \cdot 1.34670 \dots + 36 πn, t = - 18 \cdot 1.34670 \dots + 36 πn, t = 36 π - 18 \cdot 1.34670 \dots + 36 πn, t = - 36 π - 18 \cdot 1.34670 \dots + 36 πn

Graph

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