Oh, I figured it out. Turns out that 141.7 = a . So then using the eccentricity I solved for c and then for b using the relationship between the 3. Then the max is a + c and the min is b - c. :)
OK, so
.093 = 1 - \frac{b}{a}
and
.093^2 = 1 - \frac{b^2}{a^2}
But if I rewrite the first I get a = .093a+b That can't be right because I still have 2 variables.
Um, a^2 = b^2 + c^2 is the same thing as the formula I posted...
But, either way, yout idea is not right. 141.7 million is the mean distance not the distance to any point on the orbit. I think the sun is supposed to be at the focus.
Having trouble with this problem.
"The mean distance from the sun to Mars is 141.7 million miles. If the eccentricity of the orbit of Mars is .093, determine the maximum distance that Mars orbits from the sun."
So basically what it is asking for is half the length of the major axis right...
I don't want coordinates for when the value equals 0. All I want, is to convert the rectangular equation into polar form. So instead of having x and y I need r and \Theta.
Currently, I have r^2-3cos\Theta+4sin\Theta=0 but I don't know how to convert the sin and cos into polar form.
Well, actually, I guess they are the same thing, but either way, I don't know how to do it :(
As for your question, I don't see a purpose, but my teacher sure does.
I need to convert x^2+y^2-3cos\Theta+4sin\Theta=0 to polar.
Obviously the x^2+y^2 part would = r^2, but how can I get the cos and sin part to simplify?
I have to find (a+bi)(c+di) in polar form given that b,c,d>0 and a<0.
So I convert each one to polar first.
( (a+b)cis(\arctan(-b/a) + \pi) ) ( (c+d)cis(\arctan(d/c)) )
That's as far as I got. Little help please?
Yeah, I figured out the tan(x) thing. These were due today. I forget how I did the 2nd one because I didn't do it like you said. It worked some other way. What is the purpose of learning precal when the calculator already told me the answer :p
Um HallsofIvy how was the 3 seemingly unaffected by you multiplying through by sin and cos? And when I type in sin^-1(+/- root 5 / 2) I get domain error.... ?
What do you mean by let y=sin(x)?
Oh, my teacher told me sin and cos usually mess things up, but I guess that is the only option.
Edit:
I ended up with 2sin(x)^2 - 2cos(x)^2 + 3cox(x)sin(x) = 0 for the first one. That can't be right can it?
And using the identity on the 2nd one I get:
-sin(x)^2 + sin(x) +1 = 0
Then what...
I'm having trouble with two problems:
2tan(x) - 2cot(x) = -3
and
cos(x)^2 + sin(x) = 0
On the 2nd one, I can substitute 1-sin(x)^2 for cos(x)^2 right? I tried that, but it didn't work. And I have no clue what to do on the first one. Little help please?