Determine the graph of the polar equation r=4/(1-1/2cosx(theta))

  see below

Step-by-step explanation:

We assume you want the graph of ...

A graphing calculator or spreadsheet is useful for this.

__

You know cos(θ) = cos(-θ), so the graph is symmetrical about the x-axis. You can evaluate the function at a few points to find the general outline.

  r at 0° = 8

  r at 30° ≈ 7.05

  r at 45° ≈ 6.19

  r at 60° ≈ 5.33

  r at 90° = 4

  r at 120° = 3.2

  r at 135° ≈ 2.96

  r at 150° ≈ 2.79

  r at 180° ≈ 2.67

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92

step-by-step explanation:

to determine whether a given function is even, we simply substitute x with -x in the expression. if the result after simplification is identical to the original equation, then the function is said to be even other wise odd.

f(-x) = (-x)^2 - (-x) + 8

      = x^2 + x +8

the resulting function is not identical to the original one;

f(-x) ≠ f(x)

therefore, f(x) is not an even function