Trigonometry Examples

\sin (45) + \cos (45)

$\sin (45) + \cos (45)$

Step 1

Simplify each term.

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Step 1.1

The exact value of

\sin (45)

$\sin (45)$ is

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

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

\frac{\sqrt{2}}{2} + \cos (45)

$\frac{\sqrt{2}}{2} + \cos (45)$

Step 1.2

The exact value of

\cos (45)

$\cos (45)$ is

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

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

\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}

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

\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

\frac{\sqrt{2} + \sqrt{2}}{2}

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

Step 2.2

Add

\sqrt{2}

$\sqrt{2}$ and

\sqrt{2}

$\sqrt{2}$ .

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

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

Step 2.3

Cancel the common factor of

2

$2$ .

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Step 2.3.1

Cancel the common factor.

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

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

Step 2.3.2

Divide

\sqrt{2}

$\sqrt{2}$ by

1

$1$ .

\sqrt{2}

$\sqrt{2}$

\sqrt{2}

$\sqrt{2}$

\sqrt{2}

$\sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\sqrt{2}

$\sqrt{2}$

Decimal Form:

1.41421356 \dots

$1.41421356 \dots$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$