Trigonometry Examples

$\sin (210) + \tan (135)$

Step 1

Simplify each term.

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Step 1.1

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

$- \sin (30) + \tan (135)$

Step 1.2

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

$- \frac{1}{2} + \tan (135)$

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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 $- 1$ .

$\frac{- 3}{2}$

Step 6

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

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