change equations to polar form:
1) y= -1
2) x^2 + y^2 = 4
how would i do these questions? thank u
to convert to polar, you use the relationship: x = rcos(theta), and
y = rsin(theta)
1) rsin(theta) = -1,
r = 1-/sin(theta)
2)try this yourself by substituting as in part 1.
but what is theta though? i dunno the angle
don't need to know the angle. Rememeber, it's an equation of a line. As theta varies, r varies. (just like as x varies, y varies).
In the first equation, y = -1, since y is a constant value and does not vary with theta, the equation can be written as r*sin(theta) = -1. To convert to polar form, solve for r by dividing both sides of the equation by sin(theta). This gives us r = -1/sin(theta).
In the second equation, x^2 + y^2 = 4, recall that x = r*cos(theta) and y = r*sin(theta). Substitute these values into the equation and we get (r*cos(theta))^2 + (r*sin(theta))^2 = 4. Simplifying this equation gives us r^2*(cos^2(theta) + sin^2(theta)) = 4. Since cos^2(theta) + sin^2(theta) is equal to 1, the equation simplifies further to r^2 = 4.
Now, to find the equation in polar form, we just need to take the square root of both sides and get r = 2.
So, the polar form of the equations are:
1) r = -1/sin(theta)
2) r = 2