What point on the x-y plane does theta = 0 describe?
I tried doing:
tan(theta) = y/x
tan(0rad) = y/x
0 = y/x
So y is definitely 0.
y = rsin(theta)
r = y/sin(theta)
= 0/sin(0rad)
= 0/0
... I highly doubt that this problem was meant for having to do L'Hopital's rule, so I'm not sure what to do here. Thanks for any help in advance.
Do you mean "at what points does the sin of theta equal zero"?
If so, sin(Theta) = Y/r. Then sine of theta is zero at every point where Y equals zero: 0, 180, and 360o.
To determine what point on the x-y plane theta = 0 describes, let's review the trigonometric functions and their values for different angles.
In this case, theta represents the angle, and we're considering theta = 0 radians.
The function tan(theta) = y/x represents the tangent of the angle theta, where y is the length of the side opposite the angle and x is the length of the adjacent side. Since theta = 0, tan(0) = y/x.
However, we need to be cautious when dealing with trigonometric functions at certain angles. The tangent of 0 degrees (or 0 radians) is defined to be zero, but dividing by zero to find y/x is undefined and not a valid approach.
Instead, let's consider the values of the functions sin(theta) and cos(theta) at theta = 0 radians.
For sin(0), the sine of 0 degrees (or 0 radians) is defined to be zero, so sin(0) = 0.
For cos(0), the cosine of 0 degrees (or 0 radians) is defined to be 1, so cos(0) = 1.
From these values, we can determine that at theta = 0 radians, the y-coordinate (or the vertical component) is zero, and the x-coordinate (or the horizontal component) is nonzero.
Hence, the point on the x-y plane that theta = 0 describes is (x, y) = (x, 0). This represents the x-axis.