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><mo>-</mo><mn>1</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><mo>-</mo><mn>1</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><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by adding the exponents.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

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

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

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></msqrt></mstyle></math>

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></msqrt></mstyle></math>

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

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

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Rewrite <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

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

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

Opposite <math><mstyle displaystyle="true"><mo>=</mo><mn>0</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"><mn>0</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.

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 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.

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

Undefined

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.

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

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.

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

Undefined

This is the solution to each trig value.

Undefined

Do you know how to Find the Other Trig Values in Quadrant III cos(theta)=-1? 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 seventy-eight million eight hundred sixty-six thousand six hundred nine |
---|

- 2078866609 has 4 divisors, whose sum is
**2079051300** - The reverse of 2078866609 is
**9066688702** - Previous prime number is
**12041**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 52
- Digital Root 7

Name | one billion sixty-two million three hundred eighty-five thousand seven hundred sixty-one |
---|

- 1062385761 has 8 divisors, whose sum is
**1417197600** - The reverse of 1062385761 is
**1675832601** - Previous prime number is
**2099**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | seven hundred sixty-six million seven hundred thirty-nine thousand eight hundred fourteen |
---|

- 766739814 has 16 divisors, whose sum is
**1623684528** - The reverse of 766739814 is
**418937667** - Previous prime number is
**17**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 51
- Digital Root 6