Mistake on page 837

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Mistake on page 837

Faraz Rashid
On page 837 of the Precalc book (Part 2(c) of example 10.6.5), we have
f(x) = arccot(x/2) + pi
While trying to express this in terms or arctan for plotting purposes, we encounter an issue at x=0.
So, we have to resort to a piecewise function.

It is stated in the text,
"We know g(0) = arccot(0) + pi = pi and neither of the formulas for g involving arctangent will produce this result."

I think there are a couple of issues with the above statement,
--- It should be f(0) instead of g(0) in the above statement.
--- Also arccot(0) = pi/2, so the correct statement should be
"We know f(0) = arccot(0) + pi = 3pi/2 and neither of the formulas for g involving arctangent will produce this result."

And then in the mathematical expression of the piecewise function g, the middle expression should be changed from "pi, if x = 0" TO "3pi/2, if x = 0"  

 Thank you.
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Mistake on page 876 --- Question 84

Faraz Rashid
Also, for Question 84 on page 876 i.e.

(sin(x))^2 < 3/4

the solution given on page 879 seems to be for the inequality

(sin(x))^2 > 3/4
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Mistake on page 889

Faraz Rashid
Mistake on Page 889 --- Example 11.1.4 --- Part(1)

In the solution to part 1,
"cos(t) + sqrt(3) sin(t)" is rewritten as "2sin(t + pi/3)"
This isn't quite correct.

"cos(t) + sqrt(3) sin(t)" simplifies to "2sin(t + pi/6)"

But since the solution and graphs for part(1) make repeated mention of "2sin(t + pi/3)", I think it would be simpler to change the question from "cos(t) + sqrt(3) sin(t)" to "sin(t) + sqrt(3) cos(t)".
That way, "2sin(t + pi/3)" would still be the correct simplification.
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Mistake on page 931 --- Question 96

Faraz Rashid
This post was updated on .
On page 931 --- Question 96 ---

The question reads "r = 1+sin(theta)"
The answer on page 937 is given as "(x^2 + y^2 + y)^2 = x^2 + y^2"

__

Either the question should be left untouched and the answer changed to
"(x^2 + y^2 - y)^2 = x^2 + y^2"

OR

the answer should be left unchanged and the question changed to
"r = 1 - sin(theta)"

____________
Also on page 950, there is a minor typo.
In the very first pair of figures on page 950 (the theta-r plane plot and xy-plane plot).
The xy-plane plot is correctly labeled.
But, in the theta-r plot, the "boxed label 3" should be next to the part of the graph which is above the horizontal axis (theta axis).
The "boxed label 4" should refer to the part which is below the horizontal axis.

In short, the labels 3 and 4 should be exchanged in the left plot. The labels in the right plot are correct.
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Re: Mistake on page 931 --- Question 96

Carl Stitz
Administrator
Many thanks for these!

I'll send them off to Jeff to make sure they are corrected in the 4th edition.

Carl