Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = -2 + 3 cos θ

select one:
a. no symmetry
b. y-axis only
c. x-axis only
d. origin only

The graph is symmetric about the x-axis only

Step-by-step explanation:

* Lets study the limacon curve

- Equations of the form:

# r = a + b sin θ

# r = a – b sin θ

# r = a + b cos θ

# r = a – b cos θ  

All will produce limacons.    

* Lets examine what happens for various values of a and b.  

- When the value of a is less than the value of b, the graph is  

 a limacon with and inner loop.

- When the value of a is greater than the value of b, the graph is

 a dimpled limacon.

- When the value of a is greater than or equal to the value of 2b,  

 the graph is a convex limacon.

- When the value of a equals the value of b, the graph is a special  

 case of the limacon.  It is called a cardioid.

* Notice that, in each of the graphs of the liamcons, changing

 from sine to cosine does not affect the shape of the graph just its  

 orientation.  

- Equations using sine will be symmetric to the vertical axis  

- Equations using cosine are symmetric to the horizontal axis.  

∵ r = -2 + 3 cos Ф

- from the notes up the equation of cosine is symmetric to

 the horizontal axis

∴ The graph is symmetric about the x-axis only

i can answer this question sweetie!

step-by-step explanation:

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9