Scribe Post

(sine,cosine,tangent in unit circle)

hey hey! it is I ruschev, and i am the 7th scribe for today.LETS GET IT ON! shall we?

At the beginning of the class, Mr.K gave us this questions.

a. (Cos phi over 6) (Sec phi over 3) - (Tan negative phi over 4)

*Note Secavt (sec) is the reciprocal of cosine.
Example: if the answer in cosine is ( phi over 3 ) then the Sec will be ( 3 over phi ). just flip it.

I'll first start from Cosine to tangent.

we know that cosine is the x-axis and sine theta is the y-axis on the graph and phi over 6 is a radian so if you convert radian into degrees it will be 30 degrees (using converting degree and radian mr.k gave us)

heres a little drawing that i made, it is a 30 degrees and in radian this is phi over 6.

we are looking for the (cos phi over 6)

this simply means that we are looking for the


X coordinate of phi over 6 ( 30 degrees).



but how can we find the X coordiante of phi over 6?


we do the A squared + B squared = hyp squared



formula.

1 squared + B squared = 2 squared

1 + B squared = 4

( move 1 on the other side which will change it sign into + into - )

b squared = 3

( to remove the squared we have to put root sign on both sides)

so B will = root 3

so root 3 is the Adj. Now we can find sine and cosine.

sine is opp over hyp = 1/2

cosine is adj over hyp = root 3 over 2

And the question ask us, what is the cos of phi over 6? oh! it is root 3 over 2!

the next is (sec phi over 3 ).

oh wait ! sec is the reciprocal of cosine! i can just pretend that this is (cos phi over 3) and just flip the answer.

this is pretty much the same what we did earlier.

the only difference is that we have to find the opp side.


so we do the X squared + 1 squared = 2 squared again.

after doing some caculating...the opposite side should be root 3.

now we can find sine and cosine.

sine (y-axis) = root 3 over 2

cosine (x-axis) = 1 over 2

Oh! wait! the question ask us what is (sec phi over 3) cosine is 1 over 2, then the reciprocal of cosine is 2 over 1 or just 2, so the answer for (sec phi over 3 ) must be 2!


(tan negative phi over 4)


We know that tangent is sine over cosine.





since it is negative your diagram should be also at negative.

all we have to do on this part of the question is to dived sine and cosine.

lets say (phi over 4) is at 45 degrees, and you dont know what the opposite and adj. all you know is the hpy. hyp is 2.

all you have to do is use the formula x squared + x squared = hyp squared again.

x squared + x squared = 2 squared
add the x squared
2x squared = 4
dived both side by 2 because you want to get X by it self
x squared = 2
get rid off the squared by putting root on both sides
X = root 2

so opp = root 2, adj = root 2

now you know all sides!

sine = root 2 over 2
cosine = root 2 over 2

tangent = sine over cosine
tangent = (root 2 over 2) over (root 2 over 2)
tangent = 1

WAIT!!! it says tan(NEGATIVE phi over 4), so the answer must be a negative!

hmmm.. the answer is 1 but its a negative.....oh! it must be -1!!

now to multiply all the answers.

we have (root 3 over 2) (2) -(-1)
the 2's reduced and the final answer is (root 3 +1)

Then Mr.K kicked the question up a knocth!

he gave us

(2cos squared X - cosX=1)

fisrt. you move 1 on the left side making it negative

(2cos squared X - cosX-1 = 0)

then you have to factor it.

(2cosX+1) (cosX-1) = 0

you can check your factor to see if it is rigth by multiplying it.
you have to first multiply (2cosX and cosX) = 2cos squared X
then multiply (2cosX and -1) = -2cosX
then multiply (cosX and 1) = cosX
then multply (1 from -1) = -1
so you have (2cos squared X -2cosX + cosX -1) = 0
the -2cosX + cosX will be -cosX
(2cos squared X -cosX -1 = 0) (correct)

Now i know my factor is correct.

(2cosX+1) (cosX-1)

for the (2 cosX+1) we have to dived by 2 to get rid off the 2 on the front of cosX, so it will be
cosX= -1/2 (it is negative because i moved it to the other side)

we do the same thing for (cosX-1). cosX=1

Now to find the X.

CosX=-1/2 , this means that we are looking for all the x-axis that has -1/2.
CosX=1 , this means that we are looking for all the x-axis that has 1.

X= (2phi over 3) , (4 phi over 3) , zero degree , and (2 phi) .this are all the radians that have cosX=-1/2 and 1


That's all for now!!!


THE NEXT SCRIBE SHALL BE japs_world!!!!!