Trigonometry Examples

$\cot (\frac{43 π}{6}) + \sin (\frac{28 π}{3})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$\cot (\frac{7 π}{6}) + \sin (\frac{28 π}{3})$

Step 1.2

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

$\cot (\frac{π}{6}) + \sin (\frac{28 π}{3})$

Step 1.3

The exact value of $\cot (\frac{π}{6})$ is $\sqrt{3}$ .

$\sqrt{3} + \sin (\frac{28 π}{3})$

Step 1.4

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

$\sqrt{3} + \sin (\frac{4 π}{3})$

Step 1.5

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.

$\sqrt{3} - \sin (\frac{π}{3})$

Step 1.6

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

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

Step 2

To write $\sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Combine fractions.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Move $2$ to the left of $\sqrt{3}$ .

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

Step 4.2

Subtract $\sqrt{3}$ from $2 \sqrt{3}$ .

$\frac{\sqrt{3}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$