Trigonometry Examples

$2 \sin (30) \cos (60) - \tan (45)$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$2 (\frac{1}{2}) \cos (60) - \tan (45)$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

$2 (\frac{1}{2}) \cos (60) - \tan (45)$

Step 1.2.2

Rewrite the expression.

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

Step 1.3

Multiply $\cos (60)$ by $1$ .

$\cos (60) - \tan (45)$

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Multiply $- 1$ by $1$ .

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

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $2$ .

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

Step 5.2

Subtract $2$ from $1$ .

$\frac{- 1}{2}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$