Simplify each term.

Rewrite <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> in terms of sines and cosines.

Combine <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify each term.

Factor <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mi>sin</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Separate fractions.

Convert from <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> to <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>5</mn><mrow><mo>(</mo><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><mn>5</mn><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>+</mo><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>⋅</mo><mo>-</mo><mn>4</mn></mstyle></math> .

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Take the inverse sine of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from inside the sine.

Simplify the right side.

The exact value of <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to find the solution in the second quadrant.

Subtract <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>360</mn></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The period of the <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> degrees in both directions.

Set <math><mstyle displaystyle="true"><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>4</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Take the inverse tangent of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from inside the tangent.

Simplify the right side.

Evaluate <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

The tangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to find the solution in the fourth quadrant.

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>38.65980825</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The period of the <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> degrees in both directions.

The final solution is all the values that make <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>4</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Consolidate <math><mstyle displaystyle="true"><mn>360</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>180</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>180</mn><mi>n</mi></mstyle></math> .

Consolidate <math><mstyle displaystyle="true"><mn>38.65980825</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>218.65980825</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>38.65980825</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Do you know how to Solve for x in Degrees 5tan(x)sin(x)-4sin(x)=0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | three hundred forty-two million five hundred ninety-one thousand eight hundred fifty-six |
---|

- 342591856 has 64 divisors, whose sum is
**1736545392** - The reverse of 342591856 is
**658195243** - Previous prime number is
**823**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 43
- Digital Root 7

Name | one hundred eighty million one hundred thirty-eight thousand nine hundred seventy-one |
---|

- 180138971 has 4 divisors, whose sum is
**181453992** - The reverse of 180138971 is
**179831081** - Previous prime number is
**137**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 38
- Digital Root 2

Name | one billion six hundred seventy-six million three hundred ninety-four thousand seven hundred sixty-three |
---|

- 1676394763 has 4 divisors, whose sum is
**1676477968** - The reverse of 1676394763 is
**3674936761** - Previous prime number is
**34231**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 52
- Digital Root 7