Question

solve the equation for solutions in the interval [0,2π) by first solving for the trigonometric function.

(cot x - √3) (√2 sin x + 1) = 0

Answer 1

remember a*b=0 means either a=0 or b=0 or both

Answer 2

\[\cot(x)-\sqrt{3}=0 \text{ or } \sqrt{2}\sin(x)+1=0\]

Answer 3

\[\cot(x)=\sqrt{3} \text{ or } \sin(x)=\frac{-1}{\sqrt{2}}=-\frac{\sqrt{2}}{2}\]

Answer 4

for the fist equation when do we have positive for cot(x)
when we are in the quadrant 1(+,+) and in quadrant 3(-,-)
cot(x)=cos(x)/sin(x)
when does this happen \[\frac{\cos(x)}{\sin(x)}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\]
or when does this happen
\[\frac{\cos(x)}{\sin(x)}=\frac{-\frac{\sqrt{3}}{2}}{-\frac{1}{2}}\]

Answer 5

first equation*

Answer 6

\[\cot(x)=\sqrt{3} \text{ when } x=30^o \text{ or } x=210^o\]

Answer 7

ahh gotcha on the function chart cot √3 = pi/6, 7pi/6

Answer 8

\[\sin(x)=-\frac{\sqrt{2}}{2} \text{ when } x=225^o \text{ or } x=315^o\]

Answer 9

thank you for clearing that up for me myininaya :) this damn book is worthless

Answer 10

unit circle is your friend
commit it to memory

Answer 11

i even have the unit of circle chart, but its an online class so im teaching myself everything... or trying to :S

Answer 12

do you see the pattern to remember the unit circle?

Answer 13

dont so much remember the patter but i understand now what i was doing wrong :D