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 six hundred forty-nine million three hundred twenty-nine thousand fifty-five |
---|

- 1649329055 has 8 divisors, whose sum is
**2159121744** - The reverse of 1649329055 is
**5509239461** - Previous prime number is
**11**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 44
- Digital Root 8

Name | seventy-seven million four hundred fifty-eight thousand eight hundred sixty-nine |
---|

- 77458869 has 16 divisors, whose sum is
**114889600** - The reverse of 77458869 is
**96885477** - Previous prime number is
**9**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 54
- Digital Root 9

Name | one billion two hundred seventeen million seven hundred fifty-nine thousand one hundred fifty-three |
---|

- 1217759153 has 8 divisors, whose sum is
**1380456000** - The reverse of 1217759153 is
**3519577121** - Previous prime number is
**13**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 41
- Digital Root 5