Algebra Examples

$\tan^{2} (\frac{π}{4}) + 2 \cos (\frac{8 π}{3}) - \sin (\frac{13 π}{6})$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$1^{2} + 2 \cos (\frac{8 π}{3}) - \sin (\frac{13 π}{6})$

Step 1.2

One to any power is one.

$1 + 2 \cos (\frac{8 π}{3}) - \sin (\frac{13 π}{6})$

Step 1.3

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$1 + 2 \cos (\frac{2 π}{3}) - \sin (\frac{13 π}{6})$

Step 1.4

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$1 + 2 (- \cos (\frac{π}{3})) - \sin (\frac{13 π}{6})$

Step 1.5

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$1 + 2 (- \frac{1}{2}) - \sin (\frac{13 π}{6})$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$1 + 2 (\frac{- 1}{2}) - \sin (\frac{13 π}{6})$

Step 1.6.2

Cancel the common factor.

$1 + 2 (\frac{- 1}{2}) - \sin (\frac{13 π}{6})$

Step 1.6.3

Rewrite the expression.

$1 - 1 - \sin (\frac{13 π}{6})$

Step 1.7

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$1 - 1 - \sin (\frac{π}{6})$

Step 1.8

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 1$ by $2$ .

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

Step 4.2

Subtract $2$ from $2$ .

$\frac{0 - 1}{2}$

Step 4.3

Subtract $1$ from $0$ .

$\frac{- 1}{2}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$