What is the general solution for 64=81+25-90(cos(C)) ?

The general solution for 64=81+25-90(cos(C)) is C=1.08527…+2pin,C=2pi-1.08527…+2pin

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64=81+25-90(cos(C))

64 = 81 + 25 - 90 (cos (C))

C = 1.08527 \dots + 2 πn, C = 2 π - 1.08527 \dots + 2 πn

Degrees

C = 62.18186 \dots^{\circ} + 36 0^{\circ} n, C = 297.81813 \dots^{\circ} + 36 0^{\circ} n

Solution steps

64 = 81 + 25 - 90 (cos (C))

Switch sides

81 + 25 - 90 cos (C) = 64

Add the numbers:

81 + 25 = 106

- 90 cos (C) + 106 = 64

Move

106

to the right side

- 90 cos (C) + 106 = 64

Subtract

106

from both sides

- 90 cos (C) + 106 - 106 = 64 - 106

Simplify

- 90 cos (C) = - 42

- 90 cos (C) = - 42

Divide both sides by

- 90

- 90 cos (C) = - 42

Divide both sides by

- 90

\frac{- 90 cos ( C )}{- 90} = \frac{- 42}{- 90}

Simplify

\frac{- 90 cos ( C )}{- 90} = \frac{- 42}{- 90}

Simplify

\frac{- 90 cos ( C )}{- 90} : cos (C)

\frac{- 90 cos ( C )}{- 90}

Apply the fraction rule:

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

= \frac{90 cos ( C )}{90}

Divide the numbers:

\frac{90}{90} = 1

= cos (C)

Simplify

\frac{- 42}{- 90} : \frac{7}{15}

\frac{- 42}{- 90}

Apply the fraction rule:

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

= \frac{42}{90}

Cancel the common factor:

6

= \frac{7}{15}

cos (C) = \frac{7}{15}

cos (C) = \frac{7}{15}

cos (C) = \frac{7}{15}

Apply trig inverse properties

cos (C) = \frac{7}{15}

General solutions for

cos (C) = \frac{7}{15}

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

C = arccos (\frac{7}{15}) + 2 πn, C = 2 π - arccos (\frac{7}{15}) + 2 πn

C = arccos (\frac{7}{15}) + 2 πn, C = 2 π - arccos (\frac{7}{15}) + 2 πn

Show solutions in decimal form

C = 1.08527 \dots + 2 πn, C = 2 π - 1.08527 \dots + 2 πn

What is the general solution for 64=81+25-90(cos(C)) ?
The general solution for 64=81+25-90(cos(C)) is C=1.08527…+2pin,C=2pi-1.08527…+2pin