To find the <math><mstyle displaystyle="true"><mi>cot</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><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>,</mo><mn>4</mn><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><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>,</mo><mn>4</mn><mo>)</mo></mrow></mstyle></math> .

Opposite : <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math>

Adjacent : <math><mstyle displaystyle="true"><mn>2</mn><msqrt><mn>5</mn></msqrt></mstyle></math>

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><msqrt><mn>5</mn></msqrt></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Approximate the result.

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