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

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

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Separate fractions.

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

Convert from <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> to <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>csc</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

This is the trigonometric form of a complex number where <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>z</mi><mo>|</mo></mrow></mstyle></math> is the modulus and <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> is the angle created on the complex plane.

The modulus of a complex number is the distance from the origin on the complex plane.

Substitute the actual values of <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mfrac><mrow><mi>cot</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>csc</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>0</mn></mstyle></math> .

Raising <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to any positive power yields <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

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

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

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>a</mi><mi>b</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msup></mstyle></math> to distribute the exponent.

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><msup><mi>sin</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msup><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mi>sin</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msup><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><msup><mrow><mo>(</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

Separate fractions.

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

Convert from <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> to <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>csc</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> .

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

Substitute the values of <math><mstyle displaystyle="true"><mi>θ</mi><mo>=</mo><mi>arctan</mi><mrow><mo>(</mo><mfrac><mrow><mn>0</mn></mrow><mrow><mfrac><mrow><mi>cot</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>csc</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mrow></mfrac><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>z</mi><mo>|</mo></mrow><mo>=</mo><mfrac><mrow><mi>cot</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>csc</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Do you know how to Convert to Trigonometric Form (cot(t))/(csc(t)-sin(t))? 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 | one billion twenty-two million four hundred thirty-seven thousand one hundred forty-seven |
---|

- 1022437147 has 4 divisors, whose sum is
**1066890960** - The reverse of 1022437147 is
**7417342201** - Previous prime number is
**23**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 31
- Digital Root 4

Name | one billion five hundred ninety-one million one hundred twenty thousand three hundred eighteen |
---|

- 1591120318 has 4 divisors, whose sum is
**2386680480** - The reverse of 1591120318 is
**8130211951** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 31
- Digital Root 4

Name | six hundred twenty-five million nine hundred forty-six thousand one hundred twenty-two |
---|

- 625946122 has 8 divisors, whose sum is
**939137472** - The reverse of 625946122 is
**221649526** - Previous prime number is
**4591**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 37
- Digital Root 1