Use the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Replace the known values in the equation.

Raise <math><mstyle displaystyle="true"><mn>61</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>3721</mn><mo>-</mo><msup><mrow><mo>(</mo><mo>-</mo><mn>11</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>11</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>3721</mn><mo>-</mo><mn>1</mn><mo>⋅</mo><mn>121</mn></msqrt></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>121</mn></mstyle></math> .

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>3721</mn><mo>-</mo><mn>121</mn></msqrt></mstyle></math>

Subtract <math><mstyle displaystyle="true"><mn>121</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>3721</mn></mstyle></math> .

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>3600</mn></msqrt></mstyle></math>

Rewrite <math><mstyle displaystyle="true"><mn>3600</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>60</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><msup><mrow><mn>60</mn></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

Multiply.

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

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><mn>1</mn><mo>⋅</mo><mn>60</mn></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>60</mn></mstyle></math> .

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><mn>60</mn></mstyle></math>

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><mn>60</mn></mstyle></math>

Adjacent <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><mn>60</mn></mstyle></math>

Use the definition of cosine to find the value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Move the negative in front of the fraction.

Use the definition of tangent to find the value of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Dividing two negative values results in a positive value.

Use the definition of cotangent to find the value of <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Dividing two negative values results in a positive value.

Use the definition of secant to find the value of <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Move the negative in front of the fraction.

Use the definition of cosecant to find the value of <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

Move the negative in front of the fraction.

This is the solution to each trig value.

Do you know how to Find the Other Trig Values in Quadrant III sin(x)=-11/61? 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 | one billion four hundred seventy-eight million two hundred seventy-one thousand nine hundred seventy-one |
---|

- 1478271971 has 8 divisors, whose sum is
**1614615600** - The reverse of 1478271971 is
**1791728741** - Previous prime number is
**829**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 47
- Digital Root 2

Name | one hundred seventy million two hundred five thousand five hundred fifty |
---|

- 170205550 has 32 divisors, whose sum is
**377584416** - The reverse of 170205550 is
**055502071** - Previous prime number is
**37**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 25
- Digital Root 7

Name | two hundred twelve million six hundred eleven thousand two hundred thirteen |
---|

- 212611213 has 4 divisors, whose sum is
**218357500** - The reverse of 212611213 is
**312116212** - Previous prime number is
**37**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 19
- Digital Root 1