The sine function is negative in the third and fourth quadrants. The tangent function is positive in the first and third quadrants. The set of solutions for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> are limited to the third quadrant since that is the only quadrant found in both sets.

Solution is in the third quadrant.

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

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

Replace the known values in the equation.

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>24</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><msqrt><mn>576</mn><mo>+</mo><msup><mrow><mo>(</mo><mo>-</mo><mn>7</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>7</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><msqrt><mn>576</mn><mo>+</mo><mn>49</mn></msqrt></mstyle></math>

Add <math><mstyle displaystyle="true"><mn>576</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>49</mn></mstyle></math> .

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><msqrt><mn>625</mn></msqrt></mstyle></math>

Rewrite <math><mstyle displaystyle="true"><mn>625</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>25</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><msqrt><msup><mrow><mn>25</mn></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

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

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><mn>25</mn></mstyle></math>

Hypotenuse <math><mstyle displaystyle="true"><mo>=</mo><mn>25</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.

Move the negative in front of the fraction.

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

Substitute in the known values.

Move the negative in front of the fraction.

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.

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>θ</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>θ</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 Trig Functions Using Identities tan(theta)=24/7 , sin(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 | four hundred sixteen million four hundred forty thousand five hundred seventy-one |
---|

- 416440571 has 4 divisors, whose sum is
**416929632** - The reverse of 416440571 is
**175044614** - Previous prime number is
**853**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | one billion three hundred eighty-seven million four hundred twenty thousand forty-two |
---|

- 1387420042 has 16 divisors, whose sum is
**2113511040** - The reverse of 1387420042 is
**2400247831** - Previous prime number is
**563**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 31
- Digital Root 4

Name | one billion four hundred fifty-five million nine hundred thirty thousand three hundred ninety-one |
---|

- 1455930391 has 4 divisors, whose sum is
**1461466512** - The reverse of 1455930391 is
**1930395541** - Previous prime number is
**263**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 40
- Digital Root 4