Inverse Functions & Trigonometric Equations...2

[nycmathguy]

Section 5.3

 

[MathLover1]

you made an error here: u(u+1)=2
you needed to use u^2+u-2=0 and factor it completely

here is how I did it:

sec^2(x)+tan(x)=3

use Pythagorean identity sec^2(x)-tan^2(x)=1 =>sec^2(x)=tan^2(x)+1

tan^2(x)+1+tan(x)=3
tan^2(x)+1+tan(x)-3=0
tan^2(x)+tan(x)-2=0.......factor
(tan(x) - 1) (tan(x) + 2) = 0

solutions:

if tan(x) - 1= 0 =>tan(x) = 1
if tan(x) + 2= 0=>tan(x) =- 2

use inverse to find x
x = tan^-1(1)=π/4
x = tan^-1(-2)=-1.10715

general solutions are

Radians:
x=pi/4+pi*n
x=-1.10715 +pi*n
Degrees:
x=45° +180°*n,
x=-63.43494°+180°*n

 

[nycmathguy]

you made an error here: u(u+1)=2
you needed to use u^2+u-2=0 and factor it completely

here is how I did it:

sec^2(x)+tan(x)=3

use Pythagorean identity sec^2(x)-tan^2(x)=1 =>sec^2(x)=tan^2(x)+1

tan^2(x)+1+tan(x)=3
tan^2(x)+1+tan(x)-3=0
tan^2(x)+tan(x)-2=0.......factor
(tan(x) - 1) (tan(x) + 2) = 0

solutions:

if tan(x) - 1= 0 =>tan(x) = 1
if tan(x) + 2= 0=>tan(x) =- 2

use inverse to find x
x = tan^-1(1)=π/4
x = tan^-1(-2)=-1.10715

general solutions are

Radians:
x=pi/4+pi*n
x=-1.10715 +pi*n
Degrees:
x=45° +180°*n,
x=-63.43494°+180°*n

I got it right except for a minor error. Look at my work again. I even indicated that one of the answers should be negative. I do understand the procedure and wish I could do all the problems but time is limited.

 

[MathLover1]

if one of the answers should be negative, it's not a minor error

 

[nycmathguy]

if one of the answers should be negative, it's not a minor error

At Lehman College, a negative answer that should be positive or vice-versa, simply suffers a few points less. A question like this one is probably 10 points. Math professors will usually deduct about 3 or 4 points for a sign error.

 

[MathLover1]

at my college it was an F

 

[nycmathguy]

at my college it was an F

Really. Take a look at my answer.
I got the following:

x=pi/4+pi*k
x=-1.10715 +pi*k

The only exception is the negative sign for the decimal value of x. Are you saying that your professors would mark you wrong for this sign error? That's not right. Agree? Take a few points off but to give a big fat X is just messed up.

 

[MathLover1]

yes, I am saying that my professors did it to me when I was a student
I pass written exam and came to take oral exam after that ( it was mandatory)
he gave me 7 problems (all theorems and proofs), sat on my desk watching me do it
when I was on last question, on very line before last one I put - instead of +, and he say " that is wrong colleague"
it took me a second to realize mistake and I corrected it immediately, but he said "sorry, see you next time"

 

[nycmathguy]

yes, I am saying that my professors did it to me when I was a student
I pass written exam and came to take oral exam after that ( it was mandatory)
he gave me 7 problems (all theorems and proofs), sat on my desk watching me do it
when I was on last question, on very line before last one I put - instead of +, and he say " that is wrong colleague"
it took me a second to realize mistake and I corrected it immediately, but he said "sorry, see you next time"

CUNY professors at the undergraduate level are not so strict when it comes to sign error. Perhaps they are in graduate school. I stopped going to school after earning my B.A. degree. Anyway, back to work tonight. My weekend is over. My days off over. We move on to Section 5.4. We are in the center of the textbook.

Moving forward, no more than 12 questions per section. Two of the 12 questions will be applications. I would love to answer every question but my circumstances does not allow me to do so.