Draw a triangle in the plane with vertices <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac><mo>,</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>)</mo></mrow></mstyle></math> , <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and the origin. Then <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is the angle between the positive x-axis and the ray beginning at the origin and passing through <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac><mo>,</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>)</mo></mrow></mstyle></math> . Therefore, <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>arccos</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mrow><mrow><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac></mrow></mfrac></mstyle></math> .

Multiply the numerator by the reciprocal of the denominator.

One to any power is one.

Apply the product rule to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>15</mn></mrow><mrow><mn>17</mn></mrow></mfrac></mstyle></math> .

Move <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></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>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>15</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>17</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>289</mn></mrow><mrow><mn>289</mn></mrow></mfrac></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>289</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

Multiply <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>289</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>225</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>289</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mfrac><mrow><mn>64</mn></mrow><mrow><mn>289</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>64</mn></msqrt></mrow><mrow><msqrt><mn>289</mn></msqrt></mrow></mfrac></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>64</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>8</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

Rewrite <math><mstyle displaystyle="true"><mn>289</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>17</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

Cancel the common factor of <math><mstyle displaystyle="true"><mn>17</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>17</mn></mrow><mrow><mn>15</mn></mrow></mfrac></mstyle></math> into the numerator.

Factor <math><mstyle displaystyle="true"><mn>17</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>17</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>15</mn></mrow></mfrac></mstyle></math> .

Simplify the expression.

Multiply <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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