What is the general solution for 27^2=56^2+35^2-(2*56*35*cos(x)) ?

The general solution for 27^2=56^2+35^2-(2*56*35*cos(x)) is x=0.38571…+2pin,x=2pi-0.38571…+2pin

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Popular Trigonometry >

27^2=56^2+35^2-(25635*cos(x))

Solution

2 7^{2} = 5 6^{2} + 3 5^{2} - (2 \cdot 56 \cdot 35 \cdot cos (x))

Solution

x = 0.38571 \dots + 2 πn, x = 2 π - 0.38571 \dots + 2 πn

Degrees

x = 22.09969 \dots^{\circ} + 36 0^{\circ} n, x = 337.90030 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 7^{2} = 5 6^{2} + 3 5^{2} - (2 \cdot 56 \cdot 35 cos (x))

Switch sides

5 6^{2} + 3 5^{2} - 2 \cdot 56 \cdot 35 cos (x) = 2 7^{2}

Multiply the numbers:

2 \cdot 56 \cdot 35 = 3920

5 6^{2} + 3 5^{2} - 3920 cos (x) = 2 7^{2}

5 6^{2} = 3136

3136 + 3 5^{2} - 3920 cos (x) = 2 7^{2}

3 5^{2} = 1225

3136 + 1225 - 3920 cos (x) = 2 7^{2}

Add the numbers:

3136 + 1225 = 4361

- 3920 cos (x) + 4361 = 2 7^{2}

2 7^{2} = 729

- 3920 cos (x) + 4361 = 729

Move

4361

to the right side

- 3920 cos (x) + 4361 = 729

Subtract

4361

from both sides

- 3920 cos (x) + 4361 - 4361 = 729 - 4361

Simplify

- 3920 cos (x) = - 3632

- 3920 cos (x) = - 3632

Divide both sides by

- 3920

- 3920 cos (x) = - 3632

Divide both sides by

- 3920

\frac{- 3920 cos ( x )}{- 3920} = \frac{- 3632}{- 3920}

Simplify

\frac{- 3920 cos ( x )}{- 3920} = \frac{- 3632}{- 3920}

Simplify

\frac{- 3920 cos ( x )}{- 3920} : cos (x)

\frac{- 3920 cos ( x )}{- 3920}

Apply the fraction rule:

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

= \frac{3920 cos ( x )}{3920}

Divide the numbers:

\frac{3920}{3920} = 1

= cos (x)

Simplify

\frac{- 3632}{- 3920} : \frac{227}{245}

\frac{- 3632}{- 3920}

Apply the fraction rule:

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

= \frac{3632}{3920}

Cancel the common factor:

16

= \frac{227}{245}

cos (x) = \frac{227}{245}

cos (x) = \frac{227}{245}

cos (x) = \frac{227}{245}

Apply trig inverse properties

cos (x) = \frac{227}{245}

General solutions for

cos (x) = \frac{227}{245}

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

x = arccos (\frac{227}{245}) + 2 πn, x = 2 π - arccos (\frac{227}{245}) + 2 πn

x = arccos (\frac{227}{245}) + 2 πn, x = 2 π - arccos (\frac{227}{245}) + 2 πn

Show solutions in decimal form

x = 0.38571 \dots + 2 πn, x = 2 π - 0.38571 \dots + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 27^2=56^2+35^2-(2*56*35*cos(x)) ?
The general solution for 27^2=56^2+35^2-(2*56*35*cos(x)) is x=0.38571…+2pin,x=2pi-0.38571…+2pin