Trigonometry Examples

$\cot^{2} (45) - \cos (60) + 3 \tan (45)$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cot (45)$ is $1$ .

$1^{2} - \cos (60) + 3 \tan (45)$

Step 1.2

One to any power is one.

$1 - \cos (60) + 3 \tan (45)$

Step 1.3

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$1 - \frac{1}{2} + 3 \tan (45)$

Step 1.4

The exact value of $\tan (45)$ is $1$ .

$1 - \frac{1}{2} + 3 \cdot 1$

Step 1.5

Multiply $3$ by $1$ .

$1 - \frac{1}{2} + 3$

$1 - \frac{1}{2} + 3$

Step 2

Find the common denominator.

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Step 2.1

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

$\frac{1}{1} - \frac{1}{2} + 3$

Step 2.2

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

$\frac{1}{1} \cdot \frac{2}{2} - \frac{1}{2} + 3$

Step 2.3

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

$\frac{2}{2} - \frac{1}{2} + 3$

Step 2.4

Write $3$ as a fraction with denominator $1$ .

$\frac{2}{2} - \frac{1}{2} + \frac{3}{1}$

Step 2.5

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

$\frac{2}{2} - \frac{1}{2} + \frac{3}{1} \cdot \frac{2}{2}$

Step 2.6

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

$\frac{2}{2} - \frac{1}{2} + \frac{3 \cdot 2}{2}$

$\frac{2}{2} - \frac{1}{2} + \frac{3 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 - 1 + 3 \cdot 2}{2}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $3$ by $2$ .

$\frac{2 - 1 + 6}{2}$

Step 4.2

Subtract $1$ from $2$ .

$\frac{1 + 6}{2}$

Step 4.3

Add $1$ and $6$ .

$\frac{7}{2}$

$\frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{2}$

Decimal Form:

$3.5$

Mixed Number Form:

$3 \frac{1}{2}$

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