Question
Which table best represents the graph of the equation θ = 45°?
(1 point)
Responses
θ 45° 45° 45° 45°
r 1 2 3 4
θ 45° 45° 45° 45° r 1 2 3 4
θ 45° 90° 135° 180°
r 1 2 3 4
θ 45° 90° 135° 180° r 1 2 3 4
θ 45° 90° 135° 180°
r 1 1 1 1
θ 45° 90° 135° 180° r 1 1 1 1
θ 45° 47° 50° 54°
r 1 2 3 4
θ 45° 47° 50° 54° r 1 2 3 4
(1 point)
Responses
θ 45° 45° 45° 45°
r 1 2 3 4
θ 45° 45° 45° 45° r 1 2 3 4
θ 45° 90° 135° 180°
r 1 2 3 4
θ 45° 90° 135° 180° r 1 2 3 4
θ 45° 90° 135° 180°
r 1 1 1 1
θ 45° 90° 135° 180° r 1 1 1 1
θ 45° 47° 50° 54°
r 1 2 3 4
θ 45° 47° 50° 54° r 1 2 3 4
Answers
Answered by
GPT-4o mini
The equation \( \theta = 45^\circ \) represents a line in polar coordinates that extends infinitely in both directions at an angle of \( 45^\circ \) from the origin. In polar coordinates, for any given angle \( \theta \), the radius \( r \) can take any positive or negative value.
Thus, the correct representation in a table would have a constant \( \theta \) value of \( 45^\circ \) with varying \( r \) values.
The first option fits this description:
\[
\begin{array}{|c|c|c|c|c|}
\hline
\theta & 45^\circ & 45^\circ & 45^\circ & 45^\circ \\
\hline
r & 1 & 2 & 3 & 4 \\
\hline
\end{array}
\]
This table shows that for \( \theta = 45^\circ \), the radius \( r \) can take the values 1, 2, 3, and 4, which perfectly represents the graph of the equation \( \theta = 45^\circ \).
Thus, the correct representation in a table would have a constant \( \theta \) value of \( 45^\circ \) with varying \( r \) values.
The first option fits this description:
\[
\begin{array}{|c|c|c|c|c|}
\hline
\theta & 45^\circ & 45^\circ & 45^\circ & 45^\circ \\
\hline
r & 1 & 2 & 3 & 4 \\
\hline
\end{array}
\]
This table shows that for \( \theta = 45^\circ \), the radius \( r \) can take the values 1, 2, 3, and 4, which perfectly represents the graph of the equation \( \theta = 45^\circ \).