What is the general solution for cos(x+60)= 1/2 ?

The general solution for cos(x+60)= 1/2 is x=360n,x=360n+240

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cos(x+60)= 1/2

cos (x + 6 0^{\circ}) = \frac{1}{2}

x = 36 0^{\circ} n, x = 36 0^{\circ} n + 24 0^{\circ}

Radians

x = 0 + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

cos (x + 6 0^{\circ}) = \frac{1}{2}

General solutions for

cos (x + 6 0^{\circ}) = \frac{1}{2}

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}

x + 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n, x + 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

x + 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n, x + 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

Solve

x + 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n

x + 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n

Subtract

6 0^{\circ}

from both sides

x + 6 0^{\circ} - 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

Simplify

x = 36 0^{\circ} n

Solve

x + 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 24 0^{\circ}

x + 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

Move

6 0^{\circ}

to the right side

x + 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

Subtract

6 0^{\circ}

from both sides

x + 6 0^{\circ} - 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

Simplify

x + 6 0^{\circ} - 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

Simplify

x + 6 0^{\circ} - 6 0^{\circ} : x

x + 6 0^{\circ} - 6 0^{\circ}

Add similar elements:

6 0^{\circ} - 6 0^{\circ} = 0

= x

Simplify

30 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ} : 36 0^{\circ} n + 24 0^{\circ}

30 0^{\circ} + 36 0^{\circ} n - 6 0^{\circ}

Group like terms

= 36 0^{\circ} n - 6 0^{\circ} + 30 0^{\circ}

Combine the fractions

- 6 0^{\circ} + 30 0^{\circ} : 24 0^{\circ}

Apply rule

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

= \frac{- 18 0 ^{\circ} + 90 0 ^{\circ}}{3}

Add similar elements:

- 18 0^{\circ} + 90 0^{\circ} = 72 0^{\circ}

= 24 0^{\circ}

= 36 0^{\circ} n + 24 0^{\circ}

x = 36 0^{\circ} n + 24 0^{\circ}

x = 36 0^{\circ} n + 24 0^{\circ}

x = 36 0^{\circ} n + 24 0^{\circ}

x = 36 0^{\circ} n, x = 36 0^{\circ} n + 24 0^{\circ}

3 cos (θ) = - cos (θ) tan (θ)

cos (2 x) = cos (x) - cos (3 0^{\circ}) [180]

1 - 2 tan (x) = tan^{2} (x)

- 13 a \cdot sin (2 x) - 13 b \cdot cos (2 x) = 0

3 + sin (x) = 2

What is the general solution for cos(x+60)= 1/2 ?
The general solution for cos(x+60)= 1/2 is x=360n,x=360n+240