Trigonometry Examples

$\frac{\tan^{2} (225)}{3 \sin (330)}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{\tan^{2} (45)}{3 \sin (330)}$

Step 1.2

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

$\frac{1^{2}}{3 \sin (330)}$

Step 1.3

One to any power is one.

$\frac{1}{3 \sin (330)}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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 fourth quadrant.

$\frac{1}{3 (- \sin (30))}$

Step 2.2

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

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

Step 2.3

Combine exponents.

Tap for more steps...

Step 2.3.1

Factor out negative.

$\frac{1}{- (3 (\frac{1}{2}))}$

Step 2.3.2

Combine $3$ and $\frac{1}{2}$ .

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

Step 3

Cancel the common factor of $1$ and $- 1$ .

Tap for more steps...

Step 3.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{- \frac{3}{2}}$

Step 3.2

Move the negative in front of the fraction.

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- (1 (\frac{2}{3}))$

Step 5

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

$- \frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$