Find the Cosecant Given the Point (( square root of 10)/10,-(3 square root of 10)/10)

To find the <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> between the x-axis and the line between the points <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>3</mn><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> , draw the triangle between the three points <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>3</mn><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Opposite : <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>3</mn><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac></mstyle></math>

Adjacent : <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac></mstyle></math>

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mn>10</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>10</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Raise <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

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"><mo>-</mo><mfrac><mrow><mn>3</mn><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mn>3</mn><msqrt><mn>10</mn></msqrt></mstyle></math> .

Simplify the expression.

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mn>10</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>10</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Reduce the expression by cancelling the common factors.

Raise <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>90</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>90</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine the numerators over the common denominator.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Any root of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>10</mn></mrow><mrow><mn>3</mn><msqrt><mn>10</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>10</mn></mrow><mrow><mn>3</mn><msqrt><mn>10</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><msqrt><mn>10</mn></msqrt></mrow></mfrac></mstyle></math> .

Combine and simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>10</mn></mrow><mrow><mn>3</mn><msqrt><mn>10</mn></msqrt></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><msqrt><mn>10</mn></msqrt></mrow></mfrac></mstyle></math> .

Move <math><mstyle displaystyle="true"><msqrt><mn>10</mn></msqrt></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>10</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>10</mn></msqrt></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> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>10</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mn>10</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>10</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Approximate the result.

Do you know how to Find the Cosecant Given the Point (( square root of 10)/10,-(3 square root of 10)/10)? 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 | eight hundred ninety-eight million six hundred nineteen thousand six hundred nine |
---|

- 898619609 has 16 divisors, whose sum is
**972861840** - The reverse of 898619609 is
**906916898** - Previous prime number is
**61**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 56
- Digital Root 2

Name | three hundred forty-seven million four hundred forty thousand six hundred eighteen |
---|

- 347440618 has 16 divisors, whose sum is
**598440384** - The reverse of 347440618 is
**816044743** - Previous prime number is
**211**

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

Name | one billion one hundred seventy-three million nine hundred seventy thousand four hundred ninety-nine |
---|

- 1173970499 has 32 divisors, whose sum is
**1442622720** - The reverse of 1173970499 is
**9940793711** - Previous prime number is
**163**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 50
- Digital Root 5