Trigonometry Examples

$\cos (u + 2 π)$

Step 1

Use the sum formula for cosine to simplify the expression. The formula states that $\cos (A + B) = - (\cos (A) \cos (B) + \sin (A) \sin (B))$ .

$\cos (2 π) \cdot \cos (u) - \sin (2 π) \cdot \sin (u)$

Step 2

Remove parentheses.

$\cos (2 π) \cdot \cos (u) - \sin (2 π) \cdot \sin (u)$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

$\cos (0) \cdot \cos (u) - \sin (2 π) \cdot \sin (u)$

Step 3.2

The exact value of $\cos (0)$ is $1$ .

$1 \cdot \cos (u) - \sin (2 π) \cdot \sin (u)$

Step 3.3

Multiply $\cos (u)$ by $1$ .

$\cos (u) - \sin (2 π) \cdot \sin (u)$

Step 3.4

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

$\cos (u) - \sin (0) \cdot \sin (u)$

Step 3.5

The exact value of $\sin (0)$ is $0$ .

$\cos (u) - 0 \cdot \sin (u)$

Step 3.6

Multiply $- 1$ by $0$ .

$\cos (u) + 0 \cdot \sin (u)$

Step 3.7

Multiply $0$ by $\sin (u)$ .

$\cos (u) + 0$

Step 4

Add $\cos (u)$ and $0$ .

$\cos (u)$