The sine function is positive in the first and second 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 first quadrant since that is the only quadrant found in both sets.

Solution is in the first 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"><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><mn>7</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math>

Raise <math><mstyle displaystyle="true"><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.

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.

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.

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.

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.

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 | one billion eight hundred forty-seven million four hundred thirty-four thousand one hundred two |
---|

- 1847434102 has 4 divisors, whose sum is
**2771151156** - The reverse of 1847434102 is
**2014347481** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 34
- Digital Root 7

Name | two billion twenty-three million five hundred ninety-five thousand eight hundred forty-one |
---|

- 2023595841 has 8 divisors, whose sum is
**2738398624** - The reverse of 2023595841 is
**1485953202** - Previous prime number is
**67**

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

Name | one billion five hundred thirty-five million one hundred sixty-two thousand forty-five |
---|

- 1535162045 has 8 divisors, whose sum is
**1842405720** - The reverse of 1535162045 is
**5402615351** - Previous prime number is
**15901**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 32
- Digital Root 5