What is the general solution for 2cos(x)+3cos(x)-2=0 ?

The general solution for 2cos(x)+3cos(x)-2=0 is x=1.15927…+2pin,x=2pi-1.15927…+2pin

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2cos(x)+3cos(x)-2=0

2 cos (x) + 3 cos (x) - 2 = 0

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn

Degrees

x = 66.42182 \dots^{\circ} + 36 0^{\circ} n, x = 293.57817 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 cos (x) + 3 cos (x) - 2 = 0

Simplify

2 cos (x) + 3 cos (x) - 2 : 5 cos (x) - 2

2 cos (x) + 3 cos (x) - 2

Add similar elements:

2 cos (x) + 3 cos (x) = 5 cos (x)

= 5 cos (x) - 2

5 cos (x) - 2 = 0

Move

2

to the right side

5 cos (x) - 2 = 0

Add

2

to both sides

5 cos (x) - 2 + 2 = 0 + 2

Simplify

5 cos (x) = 2

5 cos (x) = 2

Divide both sides by

5

5 cos (x) = 2

Divide both sides by

5

\frac{5 cos ( x )}{5} = \frac{2}{5}

Simplify

cos (x) = \frac{2}{5}

cos (x) = \frac{2}{5}

Apply trig inverse properties

cos (x) = \frac{2}{5}

General solutions for

cos (x) = \frac{2}{5}

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

x = arccos (\frac{2}{5}) + 2 πn, x = 2 π - arccos (\frac{2}{5}) + 2 πn

x = arccos (\frac{2}{5}) + 2 πn, x = 2 π - arccos (\frac{2}{5}) + 2 πn

Show solutions in decimal form

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn

sec (\frac{5 θ}{4}) = 2, [0.2 π]

cos (x) + ∣ cos (x) ∣ = 1, - 2 π \leq x \leq 2 π

\frac{30.56}{sin ( 8 8 ^{\circ} )} = \frac{17}{sin ( x )}

sec (x + \frac{π}{4}) = - 2, - π \leq x \leq π

\frac{56}{( 7.071 \cdot 7.681 )} = cos (θ)

What is the general solution for 2cos(x)+3cos(x)-2=0 ?
The general solution for 2cos(x)+3cos(x)-2=0 is x=1.15927…+2pin,x=2pi-1.15927…+2pin