Trigonometry Examples

$\sin (π)$

Step 1

The angle $π$ is an angle where the values of the six trigonometric functions are known. Because this is the case, add $0$ to keep the value the same.

$\sin (π + 0)$

Step 2

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

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

Step 3

Remove parentheses.

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

Step 4

Simplify each term.

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Step 4.1

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

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

Step 4.2

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

$0 \cos (0) + \cos (π) \sin (0)$

Step 4.3

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

$0 \cdot 1 + \cos (π) \sin (0)$

Step 4.4

Multiply $0$ by $1$ .

$0 + \cos (π) \sin (0)$

Step 4.5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

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

Step 4.6

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

$0 - 1 \cdot 1 \sin (0)$

Step 4.7

Multiply $- 1$ by $1$ .

$0 - 1 \sin (0)$

Step 4.8

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

$0 - 1 \cdot 0$

Step 4.9

Multiply $- 1$ by $0$ .

$0 + 0$

Step 5

Add $0$ and $0$ .

$0$