What is the general solution for 11^2=6^2+7^2-2*6*7*cos(x) ?

The general solution for 11^2=6^2+7^2-2*6*7*cos(x) is x=2.01370…+2pin,x=-2.01370…+2pin

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11^2=6^2+7^2-267*cos(x)

1 1^{2} = 6^{2} + 7^{2} - 2 \cdot 6 \cdot 7 \cdot cos (x)

x = 2.01370 \dots + 2 πn, x = - 2.01370 \dots + 2 πn

Degrees

x = 115.37693 \dots^{\circ} + 36 0^{\circ} n, x = - 115.37693 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1 1^{2} = 6^{2} + 7^{2} - 2 \cdot 6 \cdot 7 cos (x)

Switch sides

6^{2} + 7^{2} - 2 \cdot 6 \cdot 7 cos (x) = 1 1^{2}

Multiply the numbers:

2 \cdot 6 \cdot 7 = 84

6^{2} + 7^{2} - 84 cos (x) = 1 1^{2}

6^{2} = 36

36 + 7^{2} - 84 cos (x) = 1 1^{2}

7^{2} = 49

36 + 49 - 84 cos (x) = 1 1^{2}

Add the numbers:

36 + 49 = 85

- 84 cos (x) + 85 = 1 1^{2}

1 1^{2} = 121

- 84 cos (x) + 85 = 121

Move

85

to the right side

- 84 cos (x) + 85 = 121

Subtract

85

from both sides

- 84 cos (x) + 85 - 85 = 121 - 85

Simplify

- 84 cos (x) = 36

- 84 cos (x) = 36

Divide both sides by

- 84

- 84 cos (x) = 36

Divide both sides by

- 84

\frac{- 84 cos ( x )}{- 84} = \frac{36}{- 84}

Simplify

\frac{- 84 cos ( x )}{- 84} = \frac{36}{- 84}

Simplify

\frac{- 84 cos ( x )}{- 84} : cos (x)

\frac{- 84 cos ( x )}{- 84}

Apply the fraction rule:

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

= \frac{84 cos ( x )}{84}

Divide the numbers:

\frac{84}{84} = 1

= cos (x)

Simplify

\frac{36}{- 84} : - \frac{3}{7}

\frac{36}{- 84}

Apply the fraction rule:

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

= - \frac{36}{84}

Cancel the common factor:

12

= - \frac{3}{7}

cos (x) = - \frac{3}{7}

cos (x) = - \frac{3}{7}

cos (x) = - \frac{3}{7}

Apply trig inverse properties

cos (x) = - \frac{3}{7}

General solutions for

cos (x) = - \frac{3}{7}

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

x = arccos (- \frac{3}{7}) + 2 πn, x = - arccos (- \frac{3}{7}) + 2 πn

x = arccos (- \frac{3}{7}) + 2 πn, x = - arccos (- \frac{3}{7}) + 2 πn

Show solutions in decimal form

x = 2.01370 \dots + 2 πn, x = - 2.01370 \dots + 2 πn

2 cos^{2} (x) + cos (x) = 1, 0 \leq x \leq 2 π

sin (\frac{θ}{2}) = \frac{7.83}{2 ( 4.35 )}

- 4 sin (c) - 2 = sin (c) + 1

cot^{2} (x) + 1 = 2

sin (x) = \frac{1}{3}, sec (y) = \frac{25}{24 , cos ( x + y )}

What is the general solution for 11^2=6^2+7^2-2*6*7*cos(x) ?
The general solution for 11^2=6^2+7^2-2*6*7*cos(x) is x=2.01370…+2pin,x=-2.01370…+2pin