English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2x)=(2(110^{12}))/((1*10^7)^2)

Solution

sin (2 x) = \frac{2 \cdot ( 1 \cdot 1 0 ^{12} )}{( 1 \cdot 1 0 ^{7} ) ^{2}}

Solution

x = \frac{0.02000 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.02000 \dots}{2} + πn

Radians

x = 0.01000 \dots + πn, x = \frac{π}{2} - \frac{0.02000 \dots}{2} + πn

Solution steps

sin (2 x) = \frac{2 ( 1 \cdot 1 0 ^{12} )}{( 1 \cdot 1 0 ^{7} ) ^{2}}

Simplify

\frac{2 \cdot 1 \cdot 1 0 ^{12}}{( 1 \cdot 1 0 ^{7} ) ^{2}} : \frac{1}{50}

\frac{2 \cdot 1 \cdot 1 0 ^{12}}{( 1 \cdot 1 0 ^{7} ) ^{2}}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{1 0 ^{12} \cdot 2}{( 1 0 ^{7} \cdot 1 ) ^{2}}

Multiply:

1 \cdot 1 0^{7} = 1 0^{7}

= \frac{1 0 ^{12} \cdot 2}{( 1 0 ^{7} ) ^{2}}

Simplify

(1 0^{7})^{2} : 1 0^{14}

(1 0^{7})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 1 0^{7 \cdot 2}

Multiply the numbers:

7 \cdot 2 = 14

= 1 0^{14}

Factor

1 0^{14} : 2^{14} \cdot 5^{14}

Factor

10 = 2 \cdot 5

= (2 \cdot 5)^{14}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

= 2^{14} \cdot 5^{14}

Factor

1 0^{12} : 2^{12} \cdot 5^{12}

Factor

10 = 2 \cdot 5

= (2 \cdot 5)^{12}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

= 2^{12} \cdot 5^{12}

= \frac{2 ^{12} \cdot 5 ^{12} \cdot 2}{2 ^{14} \cdot 5 ^{14}}

2 \cdot 2^{12} \cdot 5^{12} = 2^{13} \cdot 5^{12}

2 \cdot 2^{12} \cdot 5^{12}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2 \cdot 2^{12} = 2^{1 + 12}

= 2^{1 + 12} \cdot 5^{12}

Add the numbers:

1 + 12 = 13

= 2^{13} \cdot 5^{12}

= \frac{2 ^{13} \cdot 5 ^{12}}{2 ^{14} \cdot 5 ^{14}}

Cancel

\frac{2 ^{13} \cdot 5 ^{12}}{2 ^{14} \cdot 5 ^{14}} : \frac{1}{5 ^{2} \cdot 2}

\frac{2 ^{13} \cdot 5 ^{12}}{2 ^{14} \cdot 5 ^{14}}

Apply exponent rule:

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

\frac{2 ^{13}}{2 ^{14}} = \frac{1}{2 ^{14 - 13}}

= \frac{5 ^{12}}{5 ^{14} \cdot 2 ^{14 - 13}}

Subtract the numbers:

14 - 13 = 1

= \frac{5 ^{12}}{5 ^{14} \cdot 2}

Apply exponent rule:

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

\frac{5 ^{12}}{5 ^{14}} = \frac{1}{5 ^{14 - 12}}

= \frac{1}{2 \cdot 5 ^{14 - 12}}

Subtract the numbers:

14 - 12 = 2

= \frac{1}{5 ^{2} \cdot 2}

= \frac{1}{5 ^{2} \cdot 2}

5^{2} \cdot 2 = 50

5^{2} \cdot 2

5^{2} = 25

= 25 \cdot 2

Multiply the numbers:

25 \cdot 2 = 50

= 50

= \frac{1}{50}

Apply trig inverse properties

sin (2 x) = \frac{1}{50}

General solutions for

sin (2 x) = \frac{1}{50}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 x = arcsin (\frac{1}{50}) + 2 πn, 2 x = π - arcsin (\frac{1}{50}) + 2 πn

2 x = arcsin (\frac{1}{50}) + 2 πn, 2 x = π - arcsin (\frac{1}{50}) + 2 πn

Solve

2 x = arcsin (\frac{1}{50}) + 2 πn : x = \frac{arcsin ( \frac{1}{50} )}{2} + πn

2 x = arcsin (\frac{1}{50}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{1}{50}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{50} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( \frac{1}{50} )}{2} + πn

x = \frac{arcsin ( \frac{1}{50} )}{2} + πn

Solve

2 x = π - arcsin (\frac{1}{50}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{1}{50} )}{2} + πn

2 x = π - arcsin (\frac{1}{50}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{1}{50}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{50} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} - \frac{arcsin ( \frac{1}{50} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{1}{50} )}{2} + πn

x = \frac{arcsin ( \frac{1}{50} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{1}{50} )}{2} + πn

Show solutions in decimal form

x = \frac{0.02000 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.02000 \dots}{2} + πn

Popular Examples

1+sin(θ)=((sqrt(3)+2))/2

1 + sin (θ) = \frac{( 3 + 2 )}{2}

-cos(θ)=-cos(2θ)

- cos (θ) = - cos (2 θ)

cos(x)= 4/(sqrt(3.38^2+4^2))

cos (x) = \frac{4}{3.3 8 ^{2} + 4 ^{2}}

solvefor x,y= 1/pi arctan(x/s)+1/2 solve for

x, y = \frac{1}{π} arctan (\frac{x}{s}) + \frac{1}{2}

tan^2(θ)+8tan(θ)+6=0

tan^{2} (θ) + 8 tan (θ) + 6 = 0

sin(2x)=(2*(1*10^{12}))/((1*10^7)^2)

Solution

Solution

Popular Examples

sin(2x)=(2(110^{12}))/((1*10^7)^2)