What is the general solution for cos(57)=sin(x) ?

The general solution for cos(57)=sin(x) is x=360n+33,x=180-33+360n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(57)=sin(x)

Solution

cos (5 7^{\circ}) = sin (x)

Solution

x = 36 0^{\circ} n + 3 3^{\circ}, x = 18 0^{\circ} - 3 3^{\circ} + 36 0^{\circ} n

Radians

x = \frac{11 π}{60} + 2 πn, x = π - \frac{11 π}{60} + 2 πn

Solution steps

cos (5 7^{\circ}) = sin (x)

Switch sides

sin (x) = cos (5 7^{\circ})

Rewrite using trig identities

cos (5 7^{\circ})

Use the following identity:

cos (x) = sin (9 0^{\circ} - x)

sin (9 0^{\circ} - 5 7^{\circ})

sin (x) = sin (9 0^{\circ} - 5 7^{\circ})

Apply trig inverse properties

sin (x) = sin (9 0^{\circ} - 5 7^{\circ})

sin (x) = sin (y) \Rightarrow x = y + 2 π n, x = π - y + 2 π n

x = 9 0^{\circ} - 5 7^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} - (9 0^{\circ} - 5 7^{\circ}) + 36 0^{\circ} n

x = 9 0^{\circ} - 5 7^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} - (9 0^{\circ} - 5 7^{\circ}) + 36 0^{\circ} n

x = 9 0^{\circ} - 5 7^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 3 3^{\circ}

x = 9 0^{\circ} - 5 7^{\circ} + 36 0^{\circ} n

Simplify

9 0^{\circ} - 5 7^{\circ} + 36 0^{\circ} n : 36 0^{\circ} n + 3 3^{\circ}

9 0^{\circ} - 5 7^{\circ} + 36 0^{\circ} n

Least Common Multiplier of

2, 60 : 60

2, 60

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

60 : 2 \cdot 2 \cdot 3 \cdot 5

60

60

divides by

260 = 30 \cdot 2

= 2 \cdot 30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 5

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

2

60

= 2 \cdot 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 3 \cdot 5 = 60

= 60

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

60

For

9 0^{\circ} :

multiply the denominator and numerator by

30

9 0^{\circ} = \frac{18 0 ^{\circ} 30}{2 \cdot 30} = 9 0^{\circ}

= 9 0^{\circ} - 5 7^{\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} 30 - 342 0 ^{\circ}}{60}

Add similar elements:

540 0^{\circ} - 342 0^{\circ} = 198 0^{\circ}

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

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

x = 18 0^{\circ} - (9 0^{\circ} - 5 7^{\circ}) + 36 0^{\circ} n : x = 18 0^{\circ} - 3 3^{\circ} + 36 0^{\circ} n

x = 18 0^{\circ} - (9 0^{\circ} - 5 7^{\circ}) + 36 0^{\circ} n

Join

9 0^{\circ} - 5 7^{\circ} : 3 3^{\circ}

9 0^{\circ} - 5 7^{\circ}

Least Common Multiplier of

2, 60 : 60

2, 60

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

60 : 2 \cdot 2 \cdot 3 \cdot 5

60

60

divides by

260 = 30 \cdot 2

= 2 \cdot 30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 5

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

2

60

= 2 \cdot 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 3 \cdot 5 = 60

= 60

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

60

For

9 0^{\circ} :

multiply the denominator and numerator by

30

9 0^{\circ} = \frac{18 0 ^{\circ} 30}{2 \cdot 30} = 9 0^{\circ}

= 9 0^{\circ} - 5 7^{\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} 30 - 342 0 ^{\circ}}{60}

Add similar elements:

540 0^{\circ} - 342 0^{\circ} = 198 0^{\circ}

= 3 3^{\circ}

x = 18 0^{\circ} - 3 3^{\circ} + 36 0^{\circ} n

x = 36 0^{\circ} n + 3 3^{\circ}, x = 18 0^{\circ} - 3 3^{\circ} + 36 0^{\circ} n

Popular Examples

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

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

2cos^2(3x)-3cos(3x)=-1,0<= x<= 2pi

2 cos^{2} (3 x) - 3 cos (3 x) = - 1, 0 \leq x \leq 2 π

solvefor x,z=y^{sin(x)}solve for

x, z = y^{s i n (x)}

solvefor t,10=14+8sin((pit)/(12))solve for

t, 10 = 14 + 8 sin (\frac{π t}{12})

cos(4x)cos(x-1)=0

cos (4 x) cos (x - 1) = 0

Frequently Asked Questions (FAQ)

What is the general solution for cos(57)=sin(x) ?
The general solution for cos(57)=sin(x) is x=360n+33,x=180-33+360n