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

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

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

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

- 10452 cos (x) + 10573 = 11025

Move

10573

to the right side

- 10452 cos (x) = 452

Divide both sides by

- 10452

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

Apply trig inverse properties

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

3 sinh (x) - cosh (x) = 1

tan (4 5^{\circ} + \frac{x}{3}) = 0.58

r = a (1 + sin (x))

cos (2 x) - sin^{2} (x) - 1 = 3 sin (x)

tan (Θ) = 1.4, 18 0^{\circ} <, Θ < 27 0^{\circ}

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