1.Graph the polar equation r=3-2sin(theta)
2. Find the polar coordinates of 6 radical 3,6 for r > 0.
3. Find the rectangular coordinates of (7, 30°).
4. Write the rectangular equation in polar form.
(x – 4)2 + y2 = 16
5. Write the equation –2x + 6y = 7 in polar form.
6. Find the distance between P1(3, –195°) and P2(–4, –94°) on the polar plane. Round your answer to the nearest thousandth.
7. Write the polar equation in rectangular form.
r = –12 cos(theta)
if you know that x^2+y^2=r^2
x=r cosθ
y=r sinθ
all these fall right out.
if you want graphs, visit wolframalpha.com and say
plot r=3-2sinθ
Where do you get stuck on these?
I'm taking this same class you should add me on Facebook lol Symone kaepernick
Identify the conic section whose equation is r=6/(2-3 cos theta).
1. To graph the polar equation r = 3 - 2sin(theta), you can plot points by substituting different values of theta into the equation to get corresponding values of r. This will allow you to create a table of values. Once you have a table of values, you can plot those points on a polar coordinate system using the angle(theta) as the angle from the positive x-axis and the r value as the distance from the origin. Connecting the plotted points will form the graph of the polar equation.
2. To find the polar coordinates of (6√3, 6) for r > 0, we can use the following conversions:
- r = sqrt(x^2 + y^2)
- theta = arctan(y / x)
Substituting the given rectangular coordinates (6√3, 6) into these equations, we get:
- r = sqrt((6√3)^2 + 6^2) = sqrt(108 + 36) = sqrt(144) = 12
- theta = arctan(6 / (6√3)) = arctan(1 / √3) = 30°
So, the polar coordinates of (6√3, 6) are (r, theta) = (12, 30°).
3. To find the rectangular coordinates of (7, 30°), we can use the following conversions:
- x = r * cos(theta)
- y = r * sin(theta)
Substituting the given polar coordinates (7, 30°) into these equations, we get:
- x = 7 * cos(30°) = 7 * (√3/2) = (7√3) / 2 ≈ 6.062
- y = 7 * sin(30°) = 7 * (1/2) = 7/2 = 3.5
So, the rectangular coordinates of (7, 30°) are approximately (6.062, 3.5).
4. To write the equation (x – 4)^2 + y^2 = 16 in polar form, we can use these conversions:
- x = r * cos(theta)
- y = r * sin(theta)
Substituting these conversions into the rectangular equation, we get:
- (r * cos(theta) – 4)^2 + (r * sin(theta))^2 = 16
- r^2 * cos^2(theta) – 8r * cos(theta) + 16 + r^2 * sin^2(theta) = 16
- r^2 * (cos^2(theta) + sin^2(theta)) – 8r * cos(theta) = 0
- r^2 – 8r * cos(theta) = 0
Thus, the polar equation of (x – 4)^2 + y^2 = 16 in polar form is r^2 – 8r * cos(theta) = 0.
5. To write the equation –2x + 6y = 7 in polar form, we can use the following conversions:
- x = r * cos(theta)
- y = r * sin(theta)
Substituting these conversions into the rectangular equation, we get:
- -2(r * cos(theta)) + 6(r * sin(theta)) = 7
- -2r * cos(theta) + 6r * sin(theta) = 7
- r*(-2cos(theta) + 6sin(theta)) = 7
Therefore, the equation –2x + 6y = 7 in polar form is r*(-2cos(theta) + 6sin(theta)) = 7.
6. To find the distance between P1(3, –195°) and P2(–4, –94°) on the polar plane, we can use the following formula:
Distance = sqrt((r1^2 + r2^2) - 2(r1)(r2)(cos(theta1 - theta2)))
Substituting the given polar coordinates into the formula:
- r1 = 3, r2 = -4, theta1 = -195°, theta2 = -94°
Distance = sqrt((3^2 + (-4)^2) - 2(3)(-4)(cos(-195° - (-94°))))
= sqrt(9 + 16 + 24cos(-101°))
= sqrt(25 + 24cos(-101°))
Now, we need to calculate the value of cos(-101°). Using the identity cos(-theta) = cos(theta), we have:
- cos(-101°) = cos(101°)
Using a calculator to find cos(101°) ≈ 0.423, we can substitute this value back into the distance formula:
Distance ≈ sqrt(25 + 24 * 0.423)
≈ sqrt(25 + 10.152)
≈ sqrt(35.152)
≈ 5.928
Therefore, the distance between P1(3, –195°) and P2(–4, –94°) on the polar plane is approximately 5.928 units.
7. To write the polar equation r = -12cos(theta) in rectangular form, we can use the conversion equations:
- x = r * cos(theta)
- y = r * sin(theta)
Substituting these conversions into the polar equation, we get:
- x = (-12cos(theta)) * cos(theta) = -12cos^2(theta)
- y = (-12cos(theta)) * sin(theta) = -12cos(theta) * sin(theta)
Therefore, the polar equation r = -12cos(theta) in rectangular form is x = -12cos^2(theta) and y = -12cos(theta) * sin(theta).