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

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

Replace the known values in the equation.

Negate <math><mstyle displaystyle="true"><msqrt><msup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math> .

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><msup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

One to any power is one.

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>1</mn><mo>-</mo><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

Raising <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to any positive power yields <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>1</mn><mo>-</mo><mn>0</mn></msqrt></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><mn>0</mn></msqrt></mstyle></math>

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>1</mn></msqrt></mstyle></math>

Any root of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

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

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><mn>1</mn></mstyle></math>

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><mn>1</mn></mstyle></math>

Use the definition of sine to find the value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Substitute in the known values.

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

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

Substitute in the known values.

Division by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> results in tangent being undefined at <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Undefined

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

Substitute in the known values.

Divide <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

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

Substitute in the known values.

Division by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> results in secant being undefined at <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Undefined

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

Substitute in the known values.

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

This is the solution to each trig value.

Undefined

Do you know how to Find the Other Trig Values in Quadrant III cos(theta)=0? 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 | three hundred eighty million four hundred fifty-four thousand eighty-six |
---|

- 380454086 has 16 divisors, whose sum is
**596700000** - The reverse of 380454086 is
**680454083** - Previous prime number is
**509**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 38
- Digital Root 2

Name | one hundred seventeen million seven hundred thousand three hundred sixty-three |
---|

- 117700363 has 4 divisors, whose sum is
**128400408** - The reverse of 117700363 is
**363007711** - Previous prime number is
**11**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 28
- Digital Root 1

Name | one billion nine hundred forty-three million five hundred fifteen thousand twenty-five |
---|

- 1943515025 has 16 divisors, whose sum is
**2817450000** - The reverse of 1943515025 is
**5205153491** - Previous prime number is
**149**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 35
- Digital Root 8