Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>25</mn><msup><mi>csc</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><msup><mi>csc</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Rewrite <math><mstyle displaystyle="true"><msqrt><mfrac><mrow><mn>4</mn></mrow><mrow><mn>25</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>4</mn></msqrt></mrow><mrow><msqrt><mn>25</mn></msqrt></mrow></mfrac></mstyle></math> .

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

Simplify the denominator.

Rewrite <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

Set up each of the solutions to solve for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

The range of cosecant is <math><mstyle displaystyle="true"><mi>y</mi><mo>≤</mo><mo>-</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi><mo>≥</mo><mn>1</mn></mstyle></math> . Since <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> does not fall in this range, there is no solution.

No solution

No solution

The range of cosecant is <math><mstyle displaystyle="true"><mi>y</mi><mo>≤</mo><mo>-</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi><mo>≥</mo><mn>1</mn></mstyle></math> . Since <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> does not fall in this range, there is no solution.

No solution

No solution

Do you know how to Solve for θ in Degrees 25csc(theta)^2-4=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 | two hundred twenty-three million seven hundred sixty-nine thousand three hundred twenty-three |
---|

- 223769323 has 4 divisors, whose sum is
**233498448** - The reverse of 223769323 is
**323967322** - Previous prime number is
**23**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 37
- Digital Root 1

Name | four hundred eighty-nine million eight hundred thirty-eight thousand six hundred forty-eight |
---|

- 489838648 has 32 divisors, whose sum is
**1780375464** - The reverse of 489838648 is
**846838984** - Previous prime number is
**13**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 58
- Digital Root 4

Name | one billion seven hundred sixty-four million two hundred thirty-six thousand two hundred fifty-six |
---|

- 1764236256 has 128 divisors, whose sum is
**17862893064** - The reverse of 1764236256 is
**6526324671** - Previous prime number is
**3**

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