Find the Cosecant Given the Point ((3 square root of 13)/13,-(2 square root of 13)/13)

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><mn>3</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>2</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</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><mn>3</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><mn>3</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>2</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Opposite : <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math>

Adjacent : <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></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><mn>3</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mn>3</mn><msqrt><mn>13</mn></msqrt></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>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>13</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>13</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>13</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>13</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>13</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>117</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>169</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>117</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>169</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>2</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mn>2</mn><msqrt><mn>13</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>2</mn></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mn>13</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>2</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>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>13</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>13</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>13</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>13</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>52</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>169</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>52</mn></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>169</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine the numerators over the common denominator.

Add <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</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>13</mn></mrow><mrow><mn>2</mn><msqrt><mn>13</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>13</mn></mrow><mrow><mn>2</mn><msqrt><mn>13</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>13</mn></msqrt></mrow><mrow><msqrt><mn>13</mn></msqrt></mrow></mfrac></mstyle></math> .

Combine and simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>13</mn></mrow><mrow><mn>2</mn><msqrt><mn>13</mn></msqrt></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>13</mn></msqrt></mrow><mrow><msqrt><mn>13</mn></msqrt></mrow></mfrac></mstyle></math> .

Move <math><mstyle displaystyle="true"><msqrt><mn>13</mn></msqrt></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>13</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>13</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>13</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>13</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>13</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>13</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.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Approximate the result.

Do you know how to Find the Cosecant Given the Point ((3 square root of 13)/13,-(2 square root of 13)/13)? 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 | two billion eighty-five million two hundred four thousand three hundred seventy |
---|

- 2085204370 has 16 divisors, whose sum is
**3754003968** - The reverse of 2085204370 is
**0734025802** - Previous prime number is
**27851**

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

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

- 553106803 has 4 divisors, whose sum is
**555061528** - The reverse of 553106803 is
**308601355** - Previous prime number is
**283**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 31
- Digital Root 4

Name | one hundred sixty-seven million nine hundred fifty-four thousand eight hundred thirty-five |
---|

- 167954835 has 4 divisors, whose sum is
**179151840** - The reverse of 167954835 is
**538459761** - Previous prime number is
**15**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 48
- Digital Root 3