What is the general solution for 144=100+6.93^2-2*10*6.93*cos(x) ?

The general solution for 144=100+6.93^2-2*10*6.93*cos(x) is x=1.54175…+2pin,x=2pi-1.54175…+2pin

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144=100+6.93^2-2106.93*cos(x)

144 = 100 + 6.9 3^{2} - 2 \cdot 10 \cdot 6.93 \cdot cos (x)

x = 1.54175 \dots + 2 πn, x = 2 π - 1.54175 \dots + 2 πn

Degrees

x = 88.33591 \dots^{\circ} + 36 0^{\circ} n, x = 271.66408 \dots^{\circ} + 36 0^{\circ} n

Solution steps

144 = 100 + 6.9 3^{2} - 2 \cdot 10 \cdot 6.93 cos (x)

Switch sides

100 + 6.9 3^{2} - 2 \cdot 10 \cdot 6.93 cos (x) = 144

Multiply the numbers:

2 \cdot 10 \cdot 6.93 = 138.6

100 + 6.9 3^{2} - 138.6 cos (x) = 144

6.9 3^{2} = 48.0249

100 + 48.0249 - 138.6 cos (x) = 144

Add the numbers:

100 + 48.0249 = 148.0249

- 138.6 cos (x) + 148.0249 = 144

Move

148.0249

to the right side

- 138.6 cos (x) + 148.0249 = 144

Subtract

148.0249

from both sides

- 138.6 cos (x) + 148.0249 - 148.0249 = 144 - 148.0249

Simplify

- 138.6 cos (x) = - 4.0249

- 138.6 cos (x) = - 4.0249

Divide both sides by

- 138.6

- 138.6 cos (x) = - 4.0249

Divide both sides by

- 138.6

\frac{- 138.6 cos ( x )}{- 138.6} = \frac{- 4.0249}{- 138.6}

Simplify

cos (x) = \frac{4.0249}{138.6}

cos (x) = \frac{4.0249}{138.6}

Apply trig inverse properties

cos (x) = \frac{4.0249}{138.6}

General solutions for

cos (x) = \frac{4.0249}{138.6}

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

x = arccos (\frac{4.0249}{138.6}) + 2 πn, x = 2 π - arccos (\frac{4.0249}{138.6}) + 2 πn

x = arccos (\frac{4.0249}{138.6}) + 2 πn, x = 2 π - arccos (\frac{4.0249}{138.6}) + 2 πn

Show solutions in decimal form

x = 1.54175 \dots + 2 πn, x = 2 π - 1.54175 \dots + 2 πn

cos (2 x) = sec (x)

3 cos^{2} (x) - 6 cos (x) + 3 = 0

14 sin (x + \frac{π}{2}) + 21 tan (π - x) = 0

8 cos^{3} (x) = 8 cos (x)

4 cos (2 θ) = cos^{2} (θ) - 2

What is the general solution for 144=100+6.93^2-2*10*6.93*cos(x) ?
The general solution for 144=100+6.93^2-2*10*6.93*cos(x) is x=1.54175…+2pin,x=2pi-1.54175…+2pin