Chapter 10.4, Problem 50PE

Given $y=\frac{\sqrt{2}}{2}x$

a. What angle does the line $y=\frac{\sqrt{2}}{2}x$ make with the positive $x\text{-axis}$ ?

b. Suppose that the $x\text{-}$ and $y\text{-axes}$ are rotated through an angle of $45°$ to form the x'- and $y\text{'}\text{-axes}$ . Write the equation $y=\frac{\sqrt{2}}{2}x$ in terms of $x\text{'}$ and $y\text{'}$ .

c. Suppose that the $x\text{-}$ and $y\text{-axes}$ are rotated through an angle of $90°$ to form the $x\text{'}\text{-}$ and $y\text{'}\text{-axes}$ . Write the equation $y=\frac{\sqrt{2}}{2}x$ in terms of $x\text{'}$ and $y\text{'}$ .