Lucky Scribe

Hi! Guyzzz... This is Emile your sixth scribe for the wonderful Monday of February.I hope I can explain this to you smoothly.

Alright, let's get into the business.It's an even day today so we only have an afternoon class.To start with, Mr. K gave us some problems to solved as follows:
1.cos²x+2cosx=0; First you need to common factor it,
cosx(cosx+2)=0;there are 2 possible answers...
a. cosx=0( in radians are:3pi/2 and pi/2)Why? Because the cos theta is equal to zero in those radians.
b.cosx=-2 which is we all know that undefine because the highest value cos can have is 1 and the lowest value is -1
2.2sin²x+sinx=6
2sin²x+sinx-6=0;then
(2sinx-3)(sinx+2)=0
a.sinx=3/2 b.sinx=-2
This two have No solution because 3/2 is bigger than 1 and -2 is smaller than -1.
3.2cos²x=7cosx-3
2cos²x-7cosx+3=0
(2cosx-1)(cosx-3)=0;There are 2 possible answers
a.cosx=1/2 which is pi/3,5pi/3,7pi/3,13pi/3 etc.
b cosx=3 undefine
4. tan²x-1=0
(tanx+1)(tanx-1)=0
a.tanx=-1 which is 3pi/4, 7pi/4 etc.
b.tanx=1 which is pi/4,5pi/4 etc.

BUT, Mr. K trick us realizing that if we do that on the exam we're going to lost half a mark.Why?Simply because we don't have enough answer for those type of questions.We should notice that on exercise there was no specific domain that he gave us, so that means we just continue to give an answer but... he taught us some shortcut to do this kind of thing.Like:
1.Instead of writing many answer you can just write:
x=pi/2+kpi;let k be the integer
Since number 2 has no solution we'll just leave it like that
3.Instead of writing many answers you can just write for:
a.x=pi/3+2kpi; let k be the integer or
x=5pi/3+2kpi; let k be the integer
4.Like the others:
a.3pi/4+kpi; let k be the integer
b.pi/4+kpi; let k be the integer

After those problem solving we did another MENTAL MATH about the unit circle, which I think we're doing fine.Then we end our day by answering some questions from Ex.4. Don't forget that we have an assignment in Ex.5.

Well, I guessed that's it for me.Until your next scribe, who is Michael.