To find the value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> , use the fact that <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> then substitute in the known values.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

To find the value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> , use the fact that <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> so <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> then substitute in the known values.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

To find the value of <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> , use the fact that <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> then substitute in the known values.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

To find the value of <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> , use the fact that <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> then substitute in the known values.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The trig functions found are as follows:

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