Expand Using Sum/Difference Formulas sin(pi/2)

$\sin (\frac{π}{2})$

The angle $\frac{π}{2}$ 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.

$\sin (\frac{π}{2} + 0)$

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

$\sin (\frac{π}{2}) \cos (0) + \cos (\frac{π}{2}) \sin (0)$

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

$(1) \cos (0) + \cos (\frac{π}{2}) \sin (0)$

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

$(1) (1) + \cos (\frac{π}{2}) \sin (0)$

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$(1) (1) + (0) \sin (0)$

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

$(1) (1) + (0) (0)$

Simplify each term.

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Multiply $1$ by $1$ .

$1 + (0) (0)$

Multiply $0$ by $0$ .

$1 + 0$

Add $1$ and $0$ .

$1$

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