The graph of
[r = -5/(2 cos \theta + sin \theta)]
is a line. Find the y-intercept of this line.
Cannot make out your typing
what does "cos \theta" mean ?
is it r = -5( 2cosØ + sinØ) ???
if so, here is the graph:
http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+-5(+2cos%C3%98+%2B+sin%C3%98)
certainly not a line
However,
r = -5/(2cosθ + sinθ)
is a line.
r(2cosθ+sinθ) = -5
2x+y = -5
Now the intercept isn't so hard to find, eh?
To find the y-intercept of the line represented by the given equation, we need to substitute \(\theta = 0\) into the equation and solve for \(r\). The y-intercept occurs when \(r = 0\).
Let's plug in \(\theta = 0\) into the equation:
\[r = -5/(2 \cos(0) + \sin(0))\]
Since \(\cos(0) = 1\) and \(\sin(0) = 0\), the equation simplifies to:
\[r = -5/(2(1) + 0)\]
\[r = -5/2\]
Therefore, the y-intercept of the line is \(r = -5/2\).