Find the Exact Value sin(pi/5)cos(pi/2)+sin(pi/2)cos(pi/5)

$\sin (\frac{π}{5}) \cos (\frac{π}{2}) + \sin (\frac{π}{2}) \cos (\frac{π}{5})$

Step 1

Simplify each term.

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

$\sin (\frac{π}{5}) \cdot 0 + \sin (\frac{π}{2}) \cos (\frac{π}{5})$

Multiply $\sin (\frac{π}{5})$ by $0$ .

$0 + \sin (\frac{π}{2}) \cos (\frac{π}{5})$

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

$0 + 1 \cos (\frac{π}{5})$

Multiply $\cos (\frac{π}{5})$ by $1$ .

$0 + \cos (\frac{π}{5})$

Step 2

Add $0$ and $\cos (\frac{π}{5})$ .

$\cos (\frac{π}{5})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\cos (\frac{π}{5})$

Decimal Form:

$0.80901699 \dots$