What is the general solution for 2cos(3x+20)=2 ?

The general solution for 2cos(3x+20)=2 is x=(360n)/3-6.66666…

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2cos(3x+20)=2

2 cos (3 x + 2 0^{\circ}) = 2

x = \frac{36 0 ^{\circ} n}{3} - 6.66666 \dots^{\circ}

Radians

x = - \frac{π}{27} + \frac{2 π}{3} n

Solution steps

2 cos (3 x + 2 0^{\circ}) = 2

Divide both sides by

2

2 cos (3 x + 2 0^{\circ}) = 2

Divide both sides by

2

\frac{2 cos ( 3 x + 2 0 ^{\circ} )}{2} = \frac{2}{2}

Simplify

cos (3 x + 2 0^{\circ}) = 1

cos (3 x + 2 0^{\circ}) = 1

General solutions for

cos (3 x + 2 0^{\circ}) = 1

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

3 x + 2 0^{\circ} = 0 + 36 0^{\circ} n

3 x + 2 0^{\circ} = 0 + 36 0^{\circ} n

Solve

3 x + 2 0^{\circ} = 0 + 36 0^{\circ} n : x = \frac{36 0 ^{\circ} n}{3} - 6.66666 \dots^{\circ}

3 x + 2 0^{\circ} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

3 x + 2 0^{\circ} = 36 0^{\circ} n

Move

2 0^{\circ}

to the right side

3 x + 2 0^{\circ} = 36 0^{\circ} n

Subtract

2 0^{\circ}

from both sides

3 x + 2 0^{\circ} - 2 0^{\circ} = 36 0^{\circ} n - 2 0^{\circ}

Simplify

3 x = 36 0^{\circ} n - 2 0^{\circ}

3 x = 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

3

3 x = 36 0^{\circ} n - 2 0^{\circ}

Divide both sides by

3

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} - \frac{2 0 ^{\circ}}{3}

Simplify

\frac{3 x}{3} = \frac{36 0 ^{\circ} n}{3} - \frac{2 0 ^{\circ}}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{36 0 ^{\circ} n}{3} - \frac{2 0 ^{\circ}}{3} : \frac{36 0 ^{\circ} n}{3} - 6.66666 \dots^{\circ}

\frac{36 0 ^{\circ} n}{3} - \frac{2 0 ^{\circ}}{3}

\frac{2 0 ^{\circ}}{3} = 6.66666 \dots^{\circ}

\frac{2 0 ^{\circ}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{18 0 ^{\circ}}{9 \cdot 3}

Multiply the numbers:

9 \cdot 3 = 27

= 6.66666 \dots^{\circ}

= \frac{36 0 ^{\circ} n}{3} - 6.66666 \dots^{\circ}

x = \frac{36 0 ^{\circ} n}{3} - 6.66666 \dots^{\circ}

x = \frac{36 0 ^{\circ} n}{3} - 6.66666 \dots^{\circ}

x = \frac{36 0 ^{\circ} n}{3} - 6.66666 \dots^{\circ}

x = \frac{36 0 ^{\circ} n}{3} - 6.66666 \dots^{\circ}

cot^{2} (3 x) - 2 cot (3 x) + 1 = 0

- \frac{tanh ( n x )}{cosh ( n x )} = 0

sin (φ) = 0

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

sin (0.3 x) = 1

What is the general solution for 2cos(3x+20)=2 ?
The general solution for 2cos(3x+20)=2 is x=(360n)/3-6.66666…