To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>7</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>11</mn><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Combine the numerators over the common denominator.

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>11</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>22</mn><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>21</mn><mi>π</mi></mstyle></math> .

Move the negative in front of the fraction.

Add full rotations of <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> until the angle is between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

Evaluate <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mfrac><mrow><mn>23</mn><mi>π</mi></mrow><mrow><mn>12</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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