What is the general solution for 7^2+25^2-2(7)(25)cos(x)=24^2 ?

The general solution for 7^2+25^2-2(7)(25)cos(x)=24^2 is x=1.28700…+2pin,x=2pi-1.28700…+2pin

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7^2+25^2-2(7)(25)cos(x)=24^2

7^{2} + 2 5^{2} - 2 (7) (25) cos (x) = 2 4^{2}

x = 1.28700 \dots + 2 πn, x = 2 π - 1.28700 \dots + 2 πn

Degrees

x = 73.73979 \dots^{\circ} + 36 0^{\circ} n, x = 286.26020 \dots^{\circ} + 36 0^{\circ} n

Solution steps

7^{2} + 2 5^{2} - 2 (7) (25) cos (x) = 2 4^{2}

Multiply the numbers:

2 \cdot 7 \cdot 25 = 350

7^{2} + 2 5^{2} - 350 cos (x) = 2 4^{2}

7^{2} = 49

49 + 2 5^{2} - 350 cos (x) = 2 4^{2}

2 5^{2} = 625

49 + 625 - 350 cos (x) = 2 4^{2}

Add the numbers:

49 + 625 = 674

- 350 cos (x) + 674 = 2 4^{2}

2 4^{2} = 576

- 350 cos (x) + 674 = 576

Move

674

to the right side

- 350 cos (x) + 674 = 576

Subtract

674

from both sides

- 350 cos (x) + 674 - 674 = 576 - 674

Simplify

- 350 cos (x) = - 98

- 350 cos (x) = - 98

Divide both sides by

- 350

- 350 cos (x) = - 98

Divide both sides by

- 350

\frac{- 350 cos ( x )}{- 350} = \frac{- 98}{- 350}

Simplify

\frac{- 350 cos ( x )}{- 350} = \frac{- 98}{- 350}

Simplify

\frac{- 350 cos ( x )}{- 350} : cos (x)

\frac{- 350 cos ( x )}{- 350}

Apply the fraction rule:

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

= \frac{350 cos ( x )}{350}

Divide the numbers:

\frac{350}{350} = 1

= cos (x)

Simplify

\frac{- 98}{- 350} : \frac{7}{25}

\frac{- 98}{- 350}

Apply the fraction rule:

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

= \frac{98}{350}

Cancel the common factor:

14

= \frac{7}{25}

cos (x) = \frac{7}{25}

cos (x) = \frac{7}{25}

cos (x) = \frac{7}{25}

Apply trig inverse properties

cos (x) = \frac{7}{25}

General solutions for

cos (x) = \frac{7}{25}

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

x = arccos (\frac{7}{25}) + 2 πn, x = 2 π - arccos (\frac{7}{25}) + 2 πn

x = arccos (\frac{7}{25}) + 2 πn, x = 2 π - arccos (\frac{7}{25}) + 2 πn

Show solutions in decimal form

x = 1.28700 \dots + 2 πn, x = 2 π - 1.28700 \dots + 2 πn

tan (x) = 0.015

x, - sin (2 x) = 0

- 2 sin (x) - 2 sin (x) cos (x) = 0

6 cos^{2} (x) + 5 cos (x) + 1 = 0

tan^{4} (x) + 1 = 4 tan^{2} (x) - 2

What is the general solution for 7^2+25^2-2(7)(25)cos(x)=24^2 ?
The general solution for 7^2+25^2-2(7)(25)cos(x)=24^2 is x=1.28700…+2pin,x=2pi-1.28700…+2pin