What is the general solution for cos(60-x)=1 ?

The general solution for cos(60-x)=1 is x=-360n+60

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cos(60-x)=1

Solution

cos (6 0^{\circ} - x) = 1

Solution

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

Radians

x = \frac{π}{3} - 2 πn

Solution steps

cos (6 0^{\circ} - x) = 1

General solutions for

cos (6 0^{\circ} - x) = 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}

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

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

Solve

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

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

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

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

Move

6 0^{\circ}

to the right side

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

Subtract

6 0^{\circ}

from both sides

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

Simplify

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

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

Divide both sides by

- 1

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

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

Simplify

\frac{- x}{- 1} = \frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1} : - 36 0^{\circ} n + 6 0^{\circ}

\frac{36 0 ^{\circ} n}{- 1} - \frac{6 0 ^{\circ}}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{36 0 ^{\circ} n}{1}

Apply rule

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{6 0 ^{\circ}}{- 1}

\frac{6 0 ^{\circ}}{- 1} = - 6 0^{\circ}

\frac{6 0 ^{\circ}}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{6 0 ^{\circ}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{6 0 ^{\circ}}{1} = 6 0^{\circ}

= - 6 0^{\circ}

= - 36 0^{\circ} n - (- 6 0^{\circ})

Apply rule

- (- a) = a

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

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

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

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

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

Popular Examples

sec^2(θ)+csc^2(θ)=1

sec^{2} (θ) + csc^{2} (θ) = 1

cos(t)-sin(t)=0

cos (t) - sin (t) = 0

sin(x)-cos(x)= 1/3

sin (x) - cos (x) = \frac{1}{3}

tan^2(x)=sec(x)-1,0<= x<= 2pi

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

sin^2(θ)=2sin^2(θ/2)

sin^{2} (θ) = 2 sin^{2} (\frac{θ}{2})

Frequently Asked Questions (FAQ)

What is the general solution for cos(60-x)=1 ?
The general solution for cos(60-x)=1 is x=-360n+60