en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(11)sin(x+37.09)=1

Solution

11 sin (x + 37.0 9^{\circ}) = 1

Solution

x = 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}

+1

Radians

x = 0.30627 \dots - \frac{245 π}{1189} + 2 πn, x = π - 0.30627 \dots - \frac{245 π}{1189} + 2 πn

Solution steps

11 sin (x + 37.0 9^{\circ}) = 1

Divide both sides by

11

11 sin (x + 37.08999 \dots^{\circ}) = 1

Divide both sides by

11

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} = \frac{1}{11}

Simplify

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} = \frac{1}{11}

Simplify

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} : sin (x + 37.08999 \dots^{\circ})

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11}

Cancel the common factor:

11

= sin (x + 37.08999 \dots^{\circ})

Simplify

\frac{1}{11} : \frac{11}{11}

\frac{1}{11}

Multiply by the conjugate

\frac{11}{11}

= \frac{1 \cdot 11}{11 11}

1 \cdot 11 = 11

1111 = 11

1111

Apply radical rule:

a a = a

1111 = 11

= 11

= \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

Apply trig inverse properties

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

General solutions for

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n, x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n, x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

Solve

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n : x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n

Simplify

arcsin (\frac{11}{11}) + 36 0^{\circ} n : arcsin (\frac{1}{11}) + 36 0^{\circ} n

arcsin (\frac{11}{11}) + 36 0^{\circ} n

\frac{11}{11} = \frac{1}{11}

\frac{11}{11}

Apply radical rule:

11 = 1 1^{\frac{1}{2}}

= \frac{1 1 ^{\frac{1}{2}}}{11}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{1 1 ^{\frac{1}{2}}}{1 1 ^{1}} = \frac{1}{1 1 ^{1 - \frac{1}{2}}}

= \frac{1}{1 1 ^{1 - \frac{1}{2}}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{1 1 ^{\frac{1}{2}}}

Apply radical rule:

1 1^{\frac{1}{2}} = 11

= \frac{1}{11}

= arcsin (\frac{1}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n

Move

37.08999 \dots^{\circ}

to the right side

x + 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n

Subtract

37.08999 \dots^{\circ}

from both sides

x + 37.08999 \dots^{\circ} - 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Simplify

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Solve

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

Simplify

18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n : 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

\frac{11}{11} = \frac{1}{11}

\frac{11}{11}

Apply radical rule:

11 = 1 1^{\frac{1}{2}}

= \frac{1 1 ^{\frac{1}{2}}}{11}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{1 1 ^{\frac{1}{2}}}{1 1 ^{1}} = \frac{1}{1 1 ^{1 - \frac{1}{2}}}

= \frac{1}{1 1 ^{1 - \frac{1}{2}}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{1 1 ^{\frac{1}{2}}}

Apply radical rule:

1 1^{\frac{1}{2}} = 11

= \frac{1}{11}

= 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

Move

37.08999 \dots^{\circ}

to the right side

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

Subtract

37.08999 \dots^{\circ}

from both sides

x + 37.08999 \dots^{\circ} - 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Simplify

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Show solutions in decimal form

x = 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}

Popular Examples

cot^2(x)+3csc(x)+3=0

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

cos(2x)+cos(x)-1=0

cos (2 x) + cos (x) - 1 = 0

cos(2x)-1=-sin(2x)

cos (2 x) - 1 = - sin (2 x)

5sin(x)=sqrt(3)+3sin(x)

5 sin (x) = 3 + 3 sin (x)

cos (a) = 0.3