Trigonometry Examples

$\cos (- \frac{37 π}{6}) - \csc (- \frac{37 π}{6})$

Step 1

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

$\cos (\frac{11 π}{6}) - \csc (- \frac{37 π}{6})$

Step 2

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

$\cos (\frac{π}{6}) - \csc (- \frac{37 π}{6})$

Step 3

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2} - \csc (- \frac{37 π}{6})$

Step 4

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

$\frac{\sqrt{3}}{2} - \csc (\frac{11 π}{6})$

Step 5

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

$\frac{\sqrt{3}}{2} - - \csc (\frac{π}{6})$

Step 6

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

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

Step 7

Multiply $- (- 1 \cdot 2)$ .

Tap for more steps...

Step 7.1

Multiply $- 1$ by $2$ .

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

Step 7.2

Multiply $- 1$ by $- 2$ .

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.86602540 \dots$