Use the image to answer the question Select the equation that represents the graph point) r=4cos @ r =8 7=4 7 =8 sin @ Which table best represents the graph ofthe equation @ = 458? (1 point) 458 458 459 45: 45 909 1350 180: 450 90″ 11352 180′ 158 473 50- 154″
The Correct Answer and Explanation is:
45° | 45° | 45° |
| :– | :– | :– | :– | :– |
| r | 1 | 2 | 3 | 4 |
Explanation:
Question 2 asks to identify which table of values best represents the graph of the polar equation θ = 45°. To solve this, we need to understand what this equation signifies in the polar coordinate system.
In polar coordinates, points are located using a distance from the origin, called the radius ‘r’, and an angle from the positive horizontal axis, called ‘θ’. The equation θ = 45° sets a strict condition for every point on its graph: the angle coordinate, θ, must always be 45 degrees. The equation places no restrictions on the value of the radius ‘r’, which means ‘r’ can be any real number.
When plotted, all the points that satisfy θ = 45° form a straight line that passes through the origin and makes a 45-degree angle with the polar axis. For example, the point (r=1, θ=45°) is on this line, as is the point (r=2, θ=45°), and so on.
Now, let’s examine the provided tables:
- First Table: This table shows four points. For each point, the value of θ is consistently 45°. The value of ‘r’ changes (1, 2, 3, 4), which is perfectly acceptable since the equation does not constrain ‘r’. All these points lie on the line described by θ = 45°. Thus, this table correctly represents the equation.
- Second, Third, and Fourth Tables: All of these tables are incorrect because they list points where the angle θ is not 45°. For instance, the second table lists angles of 90°, 135°, and 180°. These points do not satisfy the fundamental condition of the equation θ = 45°.
Therefore, the only table that accurately represents a set of points on the graph of the equation θ = 45° is the first one. on the radius r, which means r can be any value. Graphically, this equation represents a straight line that passes through the origin at an angle of 45°.
The first table shows four different points. In all four points, the value of θ is constant at 45°, while the value of r changes (1, 2, 3, and 4). This perfectly matches the condition set by the equation θ = 45°. The other tables are incorrect because they show the angle θ changing, which contradicts the given equation
53.8s
As for the specific question, if you’re choosing from a list of multiple tables or equations, the correct one will depend on the graph you have.
