Trigonometry Examples

$\frac{\cos (\frac{7 π}{4})}{\sin (\frac{7 π}{4})}$

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.

$\frac{\cos (\frac{π}{4})}{\sin (\frac{7 π}{4})}$

Step 1.2

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\frac{\sqrt{2}}{2}}{\sin (\frac{7 π}{4})}$

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.

$\frac{\frac{\sqrt{2}}{2}}{- \sin (\frac{π}{4})}$

Step 2.2

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor of $\frac{\sqrt{2}}{2}$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$\frac{1}{- 1}$

Step 3.1.3

Move the negative one from the denominator of $\frac{1}{- 1}$ .

$- 1 \cdot 1$

Step 3.2

Multiply $- 1$ by $1$ .

$- 1$