Trigonometric Equations...2

[nycmathguy]

Section 5.5

 

[MathLover1]

general solutions: in given interval [0,2pi) which is

x=0
x = (3π)/2
x = π/2

 

[nycmathguy]

general solutions: in given interval [0,2pi) which is

x=0
x = (3π)/2
x = π/2

Does [0,2pi) represent solutions in one revolution?

 

[MathLover1]

1 revolution = 360 degrees = 2pi radians

so, solutions are from 0 up to almost 1 revolution (note that 2pi is not part of solution)

 

[nycmathguy]

1 revolution = 360 degrees = 2pi radians

so, solutions are from 0 up to almost 1 revolution (note that 2pi is not part of solution)

Yes, [0,2π) means that 2pi is not part of the solution.
This is indicated by the open interval symbol ), yes?

 

[MathLover1]

yes

 

[nycmathguy]

yes

Small details are important when learning anything. There's a huge difference between brackets and parentheses in the world of mathematics.

 

[MathLover1]

A bracket (sometimes called a square bracket) indicates that the endpoint is included in the interval, a parenthesis (sometimes called a round bracket) to indicate that it is not.

 

[nycmathguy]

A bracket (sometimes called a square bracket) indicates that the endpoint is included in the interval, a parenthesis (sometimes called a round bracket) to indicate that it is not.

Correct but you would be surprised to know how many students sail through Algebra 1 and 2 without ever learning this information.

 

[MathLover1]

to sail through Algebra 1 and 2 without ever learning this information is just impossible, they have to use them all the time

 

[nycmathguy]

to sail through Algebra 1 and 2 without ever learning this information is just impossible, they have to use them all the time

Do you trust me? Do you think I am crazy? If you ask any NYC public school student after taking Algebra 1 and 2 at any of the lousy high schools across the city if they know the difference between (a, b) and [a, b] or (a, b] and [a, b), they will quickly step into the TWILIGHT ZONE and turn into zombies right before your very eyes.

You were raised in another country. This makes you a lucky person. In NYC public schools, students travel from grade to grade based on promotion (forgot the actual name) and not based on merits alone. Students in NYC public schools get "promoted" from grade to grade to make room for new students in the previous grade. So, students A, B, C, and D failed Geometry but they must get "promoted" to make room for students E, F, G, and H.

For example, 4 students failed geometry but now they are stepping into trigonometry. Parents are happy. The school district receives a big financial reward for having an excellent graduation record on file but at the end of the highway, students suffer and parents have to pick up the broken pieces. Trust me, I am a victim of the NYC public schools system.

Let me share what happened to me in 1985. I took the NYPD test one year after "earning" my high school diploma. The test is mainly reading comprehension. A high school graduate should be able to pass a reading test, right?

My score, and I'll never forget it, was 58%. The passing grade was (and may still be) 70%. In fact, I have a regular high school diploma, two CUNY degrees and a third degree from the Family Radio School of the Bible and still lack the confidence needed to pass standardized exams.

A person with my educational background should not fear walking into a testing room, right? All this academic training means ABSOLUTELY NOTHING; each diploma can be used as toilet paper. So, please give me some credit. I know what I'm talking about.

Students in Calculus 1 should be in Algebra 1. Students in Algebra 1 should be in the 5th grade. Students graduating from NYC public high schools don't know how to complete a job application. In his Calculus 1 uploaded course, Professor Leonard on YouTube reminds students not to take calculus to fail algebra. This tells me that students in calculus struggle mainly due to their lack of algebra skills. You say?

 

[MathLover1]

The school district receives a big financial reward for having an excellent graduation record, and THAT is main problem here. Just give students high grade to get money, who cares if students learn something or not.

 

[nycmathguy]

The school district receives a big financial reward for having an excellent graduation record, and THAT is main problem here. Just give students high grade to get money, who cares if students learn something or not.

This is precisely my point.