Precalculus Examples

$\sin (θ + 2 π)$

Step 1

Apply the sum of angles identity.

$\sin (θ) \cos (2 π) + \cos (θ) \sin (2 π)$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$\sin (θ) \cos (0) + \cos (θ) \sin (2 π)$

Step 2.1.2

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

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

Step 2.1.3

Multiply $\sin (θ)$ by $1$ .

$\sin (θ) + \cos (θ) \sin (2 π)$

Step 2.1.4

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

$\sin (θ) + \cos (θ) \sin (0)$

Step 2.1.5

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

$\sin (θ) + \cos (θ) \cdot 0$

Step 2.1.6

Multiply $\cos (θ)$ by $0$ .

$\sin (θ) + 0$

Step 2.2

Add $\sin (θ)$ and $0$ .

$\sin (θ)$