What is the general solution for cos(x-60)=(sqrt(3))/2 ?

The general solution for cos(x-60)=(sqrt(3))/2 is x=360n+90,x=360n+390

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Popular Trigonometry >

cos(x-60)=(sqrt(3))/2

Solution

cos (x - 6 0^{\circ}) = \frac{3}{2}

Solution

x = 36 0^{\circ} n + 9 0^{\circ}, x = 36 0^{\circ} n + 39 0^{\circ}

Radians

x = \frac{π}{2} + 2 πn, x = \frac{13 π}{6} + 2 πn

Solution steps

cos (x - 6 0^{\circ}) = \frac{3}{2}

General solutions for

cos (x - 6 0^{\circ}) = \frac{3}{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} = 3 0^{\circ} + 36 0^{\circ} n, x - 6 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n

x - 6 0^{\circ} = 3 0^{\circ} + 36 0^{\circ} n, x - 6 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n

Solve

x - 6 0^{\circ} = 3 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 9 0^{\circ}

x - 6 0^{\circ} = 3 0^{\circ} + 36 0^{\circ} n

Move

6 0^{\circ}

to the right side

x - 6 0^{\circ} = 3 0^{\circ} + 36 0^{\circ} n

Add

6 0^{\circ}

to both sides

x - 6 0^{\circ} + 6 0^{\circ} = 3 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

Simplify

x - 6 0^{\circ} + 6 0^{\circ} = 3 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

3 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ} : 36 0^{\circ} n + 9 0^{\circ}

3 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

Group like terms

= 36 0^{\circ} n + 3 0^{\circ} + 6 0^{\circ}

Least Common Multiplier of

6, 3 : 6

6, 3

Least Common Multiplier (LCM)

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Multiply each factor the greatest number of times it occurs in either

6

3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

6

For

6 0^{\circ} :

multiply the denominator and numerator by

2

6 0^{\circ} = \frac{18 0 ^{\circ} 2}{3 \cdot 2} = 6 0^{\circ}

= 3 0^{\circ} + 6 0^{\circ}

Since the denominators are equal, combine the fractions:

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

= \frac{18 0 ^{\circ} + 18 0 ^{\circ} 2}{6}

Add similar elements:

18 0^{\circ} + 36 0^{\circ} = 54 0^{\circ}

= 9 0^{\circ}

Cancel the common factor:

3

= 36 0^{\circ} n + 9 0^{\circ}

x = 36 0^{\circ} n + 9 0^{\circ}

x = 36 0^{\circ} n + 9 0^{\circ}

x = 36 0^{\circ} n + 9 0^{\circ}

Solve

x - 6 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 39 0^{\circ}

x - 6 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n

Move

6 0^{\circ}

to the right side

x - 6 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n

Add

6 0^{\circ}

to both sides

x - 6 0^{\circ} + 6 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

Simplify

x - 6 0^{\circ} + 6 0^{\circ} = 33 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

33 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ} : 36 0^{\circ} n + 39 0^{\circ}

33 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

Group like terms

= 36 0^{\circ} n + 6 0^{\circ} + 33 0^{\circ}

Least Common Multiplier of

3, 6 : 6

3, 6

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Multiply each factor the greatest number of times it occurs in either

3

6

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

6

For

6 0^{\circ} :

multiply the denominator and numerator by

2

6 0^{\circ} = \frac{18 0 ^{\circ} 2}{3 \cdot 2} = 6 0^{\circ}

= 6 0^{\circ} + 33 0^{\circ}

Since the denominators are equal, combine the fractions:

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

= \frac{18 0 ^{\circ} 2 + 198 0 ^{\circ}}{6}

Add similar elements:

36 0^{\circ} + 198 0^{\circ} = 234 0^{\circ}

= 36 0^{\circ} n + 39 0^{\circ}

x = 36 0^{\circ} n + 39 0^{\circ}

x = 36 0^{\circ} n + 39 0^{\circ}

x = 36 0^{\circ} n + 39 0^{\circ}

x = 36 0^{\circ} n + 9 0^{\circ}, x = 36 0^{\circ} n + 39 0^{\circ}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for cos(x-60)=(sqrt(3))/2 ?
The general solution for cos(x-60)=(sqrt(3))/2 is x=360n+90,x=360n+390