Trigonometry Examples

$\cos (- \frac{17 π}{4}) - \sin (- \frac{3 π}{2})$

Step 1

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

$\cos (\frac{7 π}{4}) - \sin (- \frac{3 π}{2})$

Step 2

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

$\cos (\frac{π}{4}) - \sin (- \frac{3 π}{2})$

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Multiply $- 1$ by $1$ .

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.29289321 \dots$