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 | two billion ninety-two million three hundred eighty-six thousand four hundred eighty-two |
---|

- 2092386482 has 16 divisors, whose sum is
**3334561560** - The reverse of 2092386482 is
**2846832902** - Previous prime number is
**37**

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

Name | one billion forty-nine million thirty-seven thousand two hundred ninety-seven |
---|

- 1049037297 has 8 divisors, whose sum is
**1416881856** - The reverse of 1049037297 is
**7927309401** - Previous prime number is
**77**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 42
- Digital Root 6

Name | two billion fifty-nine million six hundred fifty-nine thousand three hundred fifty-two |
---|

- 2059659352 has 32 divisors, whose sum is
**6967490400** - The reverse of 2059659352 is
**2539569502** - Previous prime number is
**431**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1