Find the Secant Given the Point (( square root of 10)/10,-(3 square root of 10)/10)

$(\frac{\sqrt{10}}{10}, - \frac{3 \sqrt{10}}{10})$

To find the $\sec (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{\sqrt{10}}{10}, - \frac{3 \sqrt{10}}{10})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{\sqrt{10}}{10}, 0)$ , and $(\frac{\sqrt{10}}{10}, - \frac{3 \sqrt{10}}{10})$ .

Opposite : $- \frac{3 \sqrt{10}}{10}$

Adjacent : $\frac{\sqrt{10}}{10}$

Find the hypotenuse using Pythagorean theorem $c = \sqrt{a^{2} + b^{2}}$ .

Tap for more steps...

Apply the product rule to $\frac{\sqrt{10}}{10}$ .

$\sqrt{\frac{{\sqrt{10}}^{2}}{10^{2}} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Tap for more steps...

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\sqrt{\frac{{(10^{\frac{1}{2}})}^{2}}{10^{2}} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{\frac{10^{\frac{1}{2} \cdot 2}}{10^{2}} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Combine $\frac{1}{2}$ and $2$ .

$\sqrt{\frac{10^{\frac{2}{2}}}{10^{2}} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\sqrt{\frac{10^{\frac{2}{2}}}{10^{2}} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Rewrite the expression.

$\sqrt{\frac{10^{1}}{10^{2}} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Evaluate the exponent.

$\sqrt{\frac{10}{10^{2}} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Raise $10$ to the power of $2$ .

$\sqrt{\frac{10}{100} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Cancel the common factor of $10$ and $100$ .

Tap for more steps...

Factor $10$ out of $10$ .

$\sqrt{\frac{10 (1)}{100} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Cancel the common factors.

Tap for more steps...

Factor $10$ out of $100$ .

$\sqrt{\frac{10 \cdot 1}{10 \cdot 10} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Cancel the common factor.

$\sqrt{\frac{10 \cdot 1}{10 \cdot 10} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

Rewrite the expression.

$\sqrt{\frac{1}{10} + {(- \frac{3 \sqrt{10}}{10})}^{2}}$

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

Tap for more steps...

Apply the product rule to $- \frac{3 \sqrt{10}}{10}$ .

$\sqrt{\frac{1}{10} + {(- 1)}^{2} {(\frac{3 \sqrt{10}}{10})}^{2}}$

Apply the product rule to $\frac{3 \sqrt{10}}{10}$ .

$\sqrt{\frac{1}{10} + {(- 1)}^{2} \frac{{(3 \sqrt{10})}^{2}}{10^{2}}}$

Apply the product rule to $3 \sqrt{10}$ .

$\sqrt{\frac{1}{10} + {(- 1)}^{2} \frac{3^{2} {\sqrt{10}}^{2}}{10^{2}}}$

Simplify the expression.

Tap for more steps...

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

$\sqrt{\frac{1}{10} + 1 \frac{3^{2} {\sqrt{10}}^{2}}{10^{2}}}$

Multiply $\frac{3^{2} {\sqrt{10}}^{2}}{10^{2}}$ by $1$ .

$\sqrt{\frac{1}{10} + \frac{3^{2} {\sqrt{10}}^{2}}{10^{2}}}$

Simplify the numerator.

Tap for more steps...

Raise $3$ to the power of $2$ .

$\sqrt{\frac{1}{10} + \frac{9 {\sqrt{10}}^{2}}{10^{2}}}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Tap for more steps...

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\sqrt{\frac{1}{10} + \frac{9 {(10^{\frac{1}{2}})}^{2}}{10^{2}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{\frac{1}{10} + \frac{9 \cdot 10^{\frac{1}{2} \cdot 2}}{10^{2}}}$

Combine $\frac{1}{2}$ and $2$ .

$\sqrt{\frac{1}{10} + \frac{9 \cdot 10^{\frac{2}{2}}}{10^{2}}}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\sqrt{\frac{1}{10} + \frac{9 \cdot 10^{\frac{2}{2}}}{10^{2}}}$

Rewrite the expression.

$\sqrt{\frac{1}{10} + \frac{9 \cdot 10^{1}}{10^{2}}}$

Evaluate the exponent.

$\sqrt{\frac{1}{10} + \frac{9 \cdot 10}{10^{2}}}$

Reduce the expression by cancelling the common factors.

Tap for more steps...

Raise $10$ to the power of $2$ .

$\sqrt{\frac{1}{10} + \frac{9 \cdot 10}{100}}$

Multiply $9$ by $10$ .

$\sqrt{\frac{1}{10} + \frac{90}{100}}$

Cancel the common factor of $90$ and $100$ .

Tap for more steps...

Factor $10$ out of $90$ .

$\sqrt{\frac{1}{10} + \frac{10 (9)}{100}}$

Cancel the common factors.

Tap for more steps...

Factor $10$ out of $100$ .

$\sqrt{\frac{1}{10} + \frac{10 \cdot 9}{10 \cdot 10}}$

Cancel the common factor.

$\sqrt{\frac{1}{10} + \frac{10 \cdot 9}{10 \cdot 10}}$

Rewrite the expression.

$\sqrt{\frac{1}{10} + \frac{9}{10}}$

Combine the numerators over the common denominator.

$\sqrt{\frac{1 + 9}{10}}$

Add $1$ and $9$ .

$\sqrt{\frac{10}{10}}$

Divide $10$ by $10$ .

$\sqrt{1}$

Any root of $1$ is $1$ .

$1$

$\sec (θ) = \frac{Hypotenuse}{Adjacent}$ therefore $\sec (θ) = \frac{1}{\frac{\sqrt{10}}{10}}$ .

$\frac{1}{\frac{\sqrt{10}}{10}}$

Simplify $\sec (θ)$ .

Tap for more steps...

Multiply the numerator by the reciprocal of the denominator.

$\sec (θ) = 1 (\frac{10}{\sqrt{10}})$

Multiply $\frac{10}{\sqrt{10}}$ by $1$ .

$\sec (θ) = \frac{10}{\sqrt{10}}$

Multiply $\frac{10}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\sec (θ) = \frac{10}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Combine and simplify the denominator.

Tap for more steps...

Multiply $\frac{10}{\sqrt{10}}$ and $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\sec (θ) = \frac{10 \sqrt{10}}{\sqrt{10} \sqrt{10}}$

Raise $\sqrt{10}$ to the power of $1$ .

$\sec (θ) = \frac{10 \sqrt{10}}{\sqrt{10} \sqrt{10}}$

Raise $\sqrt{10}$ to the power of $1$ .

$\sec (θ) = \frac{10 \sqrt{10}}{\sqrt{10} \sqrt{10}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sec (θ) = \frac{10 \sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Add $1$ and $1$ .

$\sec (θ) = \frac{10 \sqrt{10}}{{\sqrt{10}}^{2}}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Tap for more steps...

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\sec (θ) = \frac{10 \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sec (θ) = \frac{10 \sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\sec (θ) = \frac{10 \sqrt{10}}{10^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\sec (θ) = \frac{10 \sqrt{10}}{10^{\frac{2}{2}}}$

Rewrite the expression.

$\sec (θ) = \frac{10 \sqrt{10}}{10}$

Evaluate the exponent.

$\sec (θ) = \frac{10 \sqrt{10}}{10}$

Cancel the common factor of $10$ .

Tap for more steps...

Cancel the common factor.

$\sec (θ) = \frac{10 \sqrt{10}}{10}$

Divide $\sqrt{10}$ by $1$ .

$\sec (θ) = \sqrt{10}$

Approximate the result.

$\sec (θ) = \sqrt{10} \approx 3.16227766$

Do you know how to Find the Secant Given the Point (( square root of 10)/10,-(3 square root of 10)/10)? 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.