3 = r cos( + 240¡ã)
x ¨C ¡Ì3 y + ? = 0
To solve these equations, we need to understand the trigonometric functions and their properties.
First, let's look at the equation 3 = r cos(θ + 240°). This equation represents a polar coordinate system, where r is the distance from the origin to a point and θ is the angle measured from the positive x-axis to the point.
The cosine function (cos) represents the ratio of the adjacent side to the hypotenuse in a right triangle. In the polar coordinate system, cos(θ) gives us the x-coordinate of the point on the unit circle with an angle θ.
In this equation, we have 3 = r cos(θ + 240°), which means the x-coordinate of the point is 3. So, we can write r cos(θ + 240°) = 3. To solve for r and θ, we need to isolate them.
Dividing both sides of the equation by cos(θ + 240°), we get r = 3 / cos(θ + 240°). Now, we have the value of r in terms of θ.
Moving on to the second equation x - √3 y + ? = 0, it is in a Cartesian coordinate system, where x and y represent the coordinates of a point in a plane.
We need to find the value of "?" that satisfies the equation. The equation represents a line in the plane. The general form of a line equation is Ax + By + C = 0, where A, B, and C are constants.
Comparing the given equation with the general form, we have A = 1, B = -√3, and C = ?. To find "?" that satisfies the equation, we need to substitute the coordinates (x, y) of any point on the line into the equation and solve for "?".
For example, let's take the point (1, 1) on the line. Substituting x = 1 and y = 1 into the equation, we get 1 - √3(1) + ? = 0. Solving for "?", we have ? = √3 - 1.
Therefore, the value of "?" that satisfies the equation x - √3 y + ? = 0 is ? = √3 - 1.