Trigonometry Examples

$\cos (x - 2 π)$

Step 1

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

$\cos (x) \cdot \cos (2 π) + \sin (x) \cdot \sin (2 π)$

Step 2

Remove parentheses.

$\cos (x) \cdot \cos (2 π) + \sin (x) \cdot \sin (2 π)$

Step 3

Simplify each term.

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Step 3.1

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

$\cos (x) \cdot \cos (0) + \sin (x) \cdot \sin (2 π)$

Step 3.2

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

$\cos (x) \cdot 1 + \sin (x) \cdot \sin (2 π)$

Step 3.3

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

$\cos (x) + \sin (x) \cdot \sin (2 π)$

Step 3.4

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

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

Step 3.5

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

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

Step 3.6

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

$\cos (x) + 0$

Step 4

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

$\cos (x)$