# Describe in words the surface whose equation is given. (assume that r is not neg

Describe in words the surface whose equation is given. (assume that r is not negative.) $$\displaystyle\theta={\frac{{\pi}}{{{4}}}}$$
a) The plane $$\displaystyle{y}=−{z}$$ where y is not negative
b) The plane $$\displaystyle{y}={z}$$ where y and z are not negative
c) The plane $$\displaystyle{y}={x}$$ where x and y are not negative
d) The plane $$\displaystyle{y}=−{x}$$ where y is not negative
e) The plane $$\displaystyle{x}={z}$$ where x and y are not negative

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Jennifer Hill
Step 1
It represents line equation in XY- plane whose equation if given by $$\displaystyle{x}={y}$$ where x and y are not negative
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Jick1984
Step 1
Since $$\displaystyle\theta$$ is the angle of x, y plane measured counter clock-wise from the $$\displaystyle+{x}-{a}\xi{s}.$$
This equation represents all points located at an angle of $$\displaystyle{\frac{{\pi}}{{{4}}}}$$ to $$\displaystyle+{x}-{a}\xi{s}$$.
This represents half plane. Since cosine and sine have same values at $$\displaystyle{\frac{{\pi}}{{{4}}}}$$ in this case, $$\displaystyle{x}={y}$$.
It means option (c) is the correct answer.