Trigonometry Examples

${(- \frac{24}{25})}^{2} + y^{2} = 1$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 1.1.1

Apply the product rule to $- \frac{24}{25}$ .

${(- 1)}^{2} {(\frac{24}{25})}^{2} + y^{2} = 1$

Step 1.1.2

Apply the product rule to $\frac{24}{25}$ .

${(- 1)}^{2} \frac{24^{2}}{25^{2}} + y^{2} = 1$

Step 1.2

Raise $- 1$ to the power of $2$ .

$1 \frac{24^{2}}{25^{2}} + y^{2} = 1$

Step 1.3

Multiply $\frac{24^{2}}{25^{2}}$ by $1$ .

$\frac{24^{2}}{25^{2}} + y^{2} = 1$

Step 1.4

Raise $24$ to the power of $2$ .

$\frac{576}{25^{2}} + y^{2} = 1$

Step 1.5

Raise $25$ to the power of $2$ .

$\frac{576}{625} + y^{2} = 1$

Step 2

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $\frac{576}{625}$ from both sides of the equation.

$y^{2} = 1 - \frac{576}{625}$

Step 2.2

Write $1$ as a fraction with a common denominator.

$y^{2} = \frac{625}{625} - \frac{576}{625}$

Step 2.3

Combine the numerators over the common denominator.

$y^{2} = \frac{625 - 576}{625}$

Step 2.4

Subtract $576$ from $625$ .

$y^{2} = \frac{49}{625}$

Step 3

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

$y = \pm \sqrt{\frac{49}{625}}$

Step 4

Simplify $\pm \sqrt{\frac{49}{625}}$ .

Tap for more steps...

Step 4.1

Rewrite $\sqrt{\frac{49}{625}}$ as $\frac{\sqrt{49}}{\sqrt{625}}$ .

$y = \pm \frac{\sqrt{49}}{\sqrt{625}}$

Step 4.2

Simplify the numerator.

Tap for more steps...

Step 4.2.1

Rewrite $49$ as $7^{2}$ .

$y = \pm \frac{\sqrt{7^{2}}}{\sqrt{625}}$

Step 4.2.2

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

$y = \pm \frac{7}{\sqrt{625}}$

Step 4.3

Simplify the denominator.

Tap for more steps...

Step 4.3.1

Rewrite $625$ as $25^{2}$ .

$y = \pm \frac{7}{\sqrt{25^{2}}}$

Step 4.3.2

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

$y = \pm \frac{7}{25}$

Step 5

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

Tap for more steps...

Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$y = \frac{7}{25}$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \frac{7}{25}$

Step 5.3

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

$y = \frac{7}{25}, - \frac{7}{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{25}, - \frac{7}{25}$

Decimal Form:

$y = 0.28, - 0.28$