Question

Use the formula sin(2x) = 2sinxcosx, with x = 3.14 (pi)/4 to find cos 3.14(pi)/4.

Answer 1

`\text{ cos }(\pi)/(4)\text{ = }\frac{\sqrt[]{2}}{2}`

Step-by-step explanation:

Here, we want to find the value of cos pi/4

We have this as follows:

`\begin{gathered} \text{ sin(2}*(\pi)/(4))\text{ = 2sin(}(\pi)/(4))\cos (\pi)/(4) \\ \\ =\text{ sin}(\pi)/(2)\text{ = 2sin}(\pi)/(4)\cos (\pi)/(4) \end{gathered}`

Now, we have to divide both sides by 2sin(pi/4)

We have this as:

`\begin{gathered} \text{ cos}(\pi)/(4)\text{ = }(\sin (\pi)/(2))/(2\sin (\pi)/(4))=\text{ }\frac{1}{2*\frac{1}{\sqrt[]{2}}} \\ \\ \cos \text{ }(\pi)/(4)\text{ = }\frac{1}{\frac{2}{\sqrt[]{2}}}\text{ = 1}*\frac{\sqrt[]{2}}{2}\text{ = }\frac{\sqrt[]{2}}{2} \end{gathered}`