Find the Value Using the Unit Circle sec(pi/4)

Solve Math

Trigonometry

$\sec (\frac{π}{4})$

Find the value using the definition of secant.

$\sec (\frac{π}{4}) = \frac{hypotenuse}{adjacent}$

Substitute the values into the definition.

$\sec (\frac{π}{4}) = \frac{1}{\frac{\sqrt{2}}{2}}$

Simplify the result.

Tap for more steps...

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{2}{\sqrt{2}}$

Multiply $\frac{2}{\sqrt{2}}$ by $1$ .

$\frac{2}{\sqrt{2}}$

Multiply $\frac{2}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Combine and simplify the denominator.

Tap for more steps...

Multiply $\frac{2}{\sqrt{2}}$ and $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{2 \sqrt{2}}{\sqrt{2} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{2 \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{2 \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

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

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

Add $1$ and $1$ .

$\frac{2 \sqrt{2}}{{\sqrt{2}}^{2}}$

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

Tap for more steps...

Rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{2 \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

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

$\frac{2 \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 \sqrt{2}}{2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\frac{2 \sqrt{2}}{2^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\frac{2 \sqrt{2}}{2^{1}}$

Evaluate the exponent.

$\frac{2 \sqrt{2}}{2}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\frac{2 \sqrt{2}}{2}$

Divide $\sqrt{2}$ by $1$ .

$\sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

Do you know how to Find the Value Using the Unit Circle sec(pi/4)? 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.

Evaluate square root of 95^2-30^2

Find where Undefined/Discontinuous 2sin(3x)- square root of 3=0

Graph -2x-5=3

Graph -cot(x)

Solve Graphically 2sec(x)+5=9