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NationalTutoringObservatory
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MathEd-PII

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8
volunteer
great!
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volunteer
now how much do you know about the unit circle?
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student
not much, im pretty bad at it
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volunteer
thats fine
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volunteer
so ill just draw it rq
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volunteer
a trick that we can use is that we only need to memorize the first quadrant
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volunteer
and then flip the sin and cos values based on the theta values that are given
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volunteer
so do you know the values in the first quadrant?
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volunteer
not quite
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volunteer
so ill write them out for you
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volunteer
so when getting sin and cos
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volunteer
think sin as y value
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volunteer
and cos as x value
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volunteer
those are the values of theta
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volunteer
so if you put cos(ppi/6)
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volunteer
you would get sqrt(3)/2
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volunteer
and if you put sin(pi/6) you would get .5
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student
sorry i just couldnt tell what values were under pi
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volunteer
so another thing you can use is that cos and sin will either be sqrt(3)/2 or 1/2 as long as the denominator is not 4
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volunteer
oh ok
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student
thank you sorry
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volunteer
no worries, if something isnt clear feel free to tell me
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volunteer
if the denominator is 4 for the theta value, then the value of sin and cos will either be -sqty(2)/2 or sqrt(2)/2
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volunteer
an example would be theta = 5pi/4
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volunteer
or this line
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volunteer
what we can do to think about the sin and cos values would be flipping the line theta = pi/4 over the y axis
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volunteer
then flip it again over the x axis
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volunteer
if you flip over the x axis, you multiply the y value by -1
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volunteer
and if you flip over the y axis, you multiply the x value by -1
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volunteer
does that kind of make sense
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student
yes
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volunteer
great!
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volunteer
now once we get our sin and/or cos value, we can plug them into the other trig functons
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volunteer
so how about you try question 50?
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student
ok
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volunteer
how are you doing so far with this question?
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volunteer
oh sorry i didnt see you work down there
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volunteer
alright, so not quite
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volunteer
do you remember what happens if we raise something to the power of 0?
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student
it turns into 0
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student
o wait 1
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volunteer
yeaa
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volunteer
also, is tanx = (cosx/sinx)?
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student
no.... :( sin(x)/cos(x)
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volunteer
yeaa
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volunteer
lets go back to the unit circle rq
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volunteer
can you use a colored line to show where theta= 0 is
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volunteer
nicee
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volunteer
so what would the cos value be?
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volunteer
yup
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volunteer
now if cos 0 is 1, what is sin0
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volunteer
yup
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volunteer
so using that, what would sec0 be and what would tan0 be
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volunteer
tan0 is correct
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volunteer
but lets check sec again
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volunteer
what is secx?
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volunteer
now what would we get if we put in 0 for secx
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volunteer
yeaa
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volunteer
so what is our final answeR>
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volunteer
answer?*
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student
4?
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volunteer
nice!
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volunteer
do you want to try 49?
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student
yes please
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student
i will take a second
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volunteer
looks right to me
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volunteer
is it fine if I erase the board?
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student
Yes
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volunteer
great
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volunteer
now lets move onto 52
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volunteer
let me work it out myself then ill get back to you
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student
ok
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volunteer
sorry for the wait
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student
that totally ok
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volunteer
did you try while i was solving it?
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student
*is
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student
kinda
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volunteer
alright
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volunteer
so I did this in a more complex way than needed, but I think I know the easier way
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volunteer
so what was your first step?
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student
my teacher said it was wrong
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volunteer
said what was wrong?
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student
and after that i had no idea what to do
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student
my answer to this question
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volunteer
ah
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student
its an old test im looking over
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volunteer
well it would help to see exactly where you got it wrong so that we can fix that error
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student
here I can upload it onto my screen really quick
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volunteer
alright
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student
its on there, but I can't rotate it
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volunteer
i see the question, but II dont see your work
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volunteer
ah i see
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volunteer
you put in 2 instead of a
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volunteer
since the limit was where x goes to a
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volunteer
also with substitution, you got 0/0 which is an indeterminate form
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student
the pencil is me and the blue -2 and slash mark are from my teachers
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student
*teacher
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volunteer
good to know
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volunteer
I do see that you subbed in 2 for x though
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student
?
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