What is the general solution for 4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x) ?

The general solution for 4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x) is x=1.53389…+2pin,x=2pi-1.53389…+2pin

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4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x)

4.5 8^{2} = 3. 3^{2} + 3. 3^{2} - 2 (3.3) (3.3) cos (x)

x = 1.53389 \dots + 2 πn, x = 2 π - 1.53389 \dots + 2 πn

Solution steps

4.5 8^{2} = 3. 3^{2} + 3. 3^{2} - 2 (3.3) (3.3) cos (x)

Switch sides

3. 3^{2} + 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x) = 4.5 8^{2}

Simplify

3. 3^{2} + 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x) : 21.78 - 21.78 cos (x)

Simplify

4.5 8^{2} : 20.9764

21.78 - 21.78 cos (x) = 20.9764

Move

21.78

to the right side

- 21.78 cos (x) = - 0.8036

Divide both sides by

- 21.78

cos (x) = \frac{0.8036}{21.78}

Apply trig inverse properties

x = arccos (\frac{0.8036}{21.78}) + 2 πn, x = 2 π - arccos (\frac{0.8036}{21.78}) + 2 πn

Show solutions in decimal form

x = 1.53389 \dots + 2 πn, x = 2 π - 1.53389 \dots + 2 πn

y, 3 tan (y) - 4 = \frac{2}{5}

4 - 3 sin (θ) = 7

sin (x) cos (x) = - \frac{1}{4}, 0 \leq x \leq 2 π

tan (x) = (\frac{4}{3})

cos (2 x) - sin^{2} (x) - 1 = 0

What is the general solution for 4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x) ?
The general solution for 4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x) is x=1.53389…+2pin,x=2pi-1.53389…+2pin