Question

Which point forms a terminal side with the origin that creates an angle with a sin of √2 / 2 and a cosine of √2 / 2

Answer 1

We are asked to find out which point forms a terminal side with the origin that creates an angle such that the value of sin and cos is √2/2

Notice that the value of sin and cos is positive, this means that the point must be in the 1st quadrant.

Since sin and cos are positive in the 1st quadrant.

Let us find out the corresponding angle of √2/2

`\begin{gathered} \theta=\sin ^(-1)(\frac{\sqrt[]{2}}{2})=45\degree=(\pi)/(4)\: \text{radians} \\ \theta=\cos ^(-1)\sin ^{}(\frac{\sqrt[]{2}}{2})=45\degree=(\pi)/(4)\: \text{radians} \end{gathered}`

So, the angle is 45° or π/4 radians

This is exactly half of the 1st quadrant so the point must be in the middle of the first quadrant.

As you can see, point D is in the middle of the 1st quadrant.

Therefore, the correct is point D