What is the general solution for 10.5^2=6.7^2+7.8^2-2*6.7*7.8*cos(x) ?

The general solution for 10.5^2=6.7^2+7.8^2-2*6.7*7.8*cos(x) is x=1.61405…+2pin,x=-1.61405…+2pin

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Popular >

10.5^2=6.7^2+7.8^2-26.77.8*cos(x)

Solution

10. 5^{2} = 6. 7^{2} + 7. 8^{2} - 2 \cdot 6.7 \cdot 7.8 \cdot cos (x)

Solution

x = 1.61405 \dots + 2 πn, x = - 1.61405 \dots + 2 πn

Degrees

x = 92.47854 \dots^{\circ} + 36 0^{\circ} n, x = - 92.47854 \dots^{\circ} + 36 0^{\circ} n

Solution steps

10. 5^{2} = 6. 7^{2} + 7. 8^{2} - 2 \cdot 6.7 \cdot 7.8 cos (x)

Switch sides

6. 7^{2} + 7. 8^{2} - 2 \cdot 6.7 \cdot 7.8 cos (x) = 10. 5^{2}

Multiply the numbers:

2 \cdot 6.7 \cdot 7.8 = 104.52

6. 7^{2} + 7. 8^{2} - 104.52 cos (x) = 10. 5^{2}

6. 7^{2} = 44.89

44.89 + 7. 8^{2} - 104.52 cos (x) = 10. 5^{2}

7. 8^{2} = 60.84

44.89 + 60.84 - 104.52 cos (x) = 10. 5^{2}

Add the numbers:

44.89 + 60.84 = 105.73

- 104.52 cos (x) + 105.73 = 10. 5^{2}

10. 5^{2} = 110.25

- 104.52 cos (x) + 105.73 = 110.25

Multiply both sides by

100

- 104.52 cos (x) + 105.73 = 110.25

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- 104.52 cos (x) \cdot 100 + 105.73 \cdot 100 = 110.25 \cdot 100

Refine

- 10452 cos (x) + 10573 = 11025

- 10452 cos (x) + 10573 = 11025

Move

10573

to the right side

- 10452 cos (x) + 10573 = 11025

Subtract

10573

from both sides

- 10452 cos (x) + 10573 - 10573 = 11025 - 10573

Simplify

- 10452 cos (x) = 452

- 10452 cos (x) = 452

Divide both sides by

- 10452

- 10452 cos (x) = 452

Divide both sides by

- 10452

\frac{- 10452 cos ( x )}{- 10452} = \frac{452}{- 10452}

Simplify

\frac{- 10452 cos ( x )}{- 10452} = \frac{452}{- 10452}

Simplify

\frac{- 10452 cos ( x )}{- 10452} : cos (x)

\frac{- 10452 cos ( x )}{- 10452}

Apply the fraction rule:

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

= \frac{10452 cos ( x )}{10452}

Divide the numbers:

\frac{10452}{10452} = 1

= cos (x)

Simplify

\frac{452}{- 10452} : - \frac{113}{2613}

\frac{452}{- 10452}

Apply the fraction rule:

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

= - \frac{452}{10452}

Cancel the common factor:

4

= - \frac{113}{2613}

cos (x) = - \frac{113}{2613}

cos (x) = - \frac{113}{2613}

cos (x) = - \frac{113}{2613}

Apply trig inverse properties

cos (x) = - \frac{113}{2613}

General solutions for

cos (x) = - \frac{113}{2613}

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

x = arccos (- \frac{113}{2613}) + 2 πn, x = - arccos (- \frac{113}{2613}) + 2 πn

x = arccos (- \frac{113}{2613}) + 2 πn, x = - arccos (- \frac{113}{2613}) + 2 πn

Show solutions in decimal form

x = 1.61405 \dots + 2 πn, x = - 1.61405 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 10.5^2=6.7^2+7.8^2-2*6.7*7.8*cos(x) ?
The general solution for 10.5^2=6.7^2+7.8^2-2*6.7*7.8*cos(x) is x=1.61405…+2pin,x=-1.61405…+2pin