Question

Find the equation of the tangent line
y= 1/cosx - 2cosx at (pi/3, 1)

Answer 1

I think i did my derivative wrong
i got 2 tan^2 (x) / cosx

Answer 2

take the derivitave then plug in your x value to get slope, then use y = mx+b with your one point to figure out b

Answer 3

I know what to do , but i just got the answer wrong..

Answer 4

what's your slope?

Answer 5

Shouldn't you have two different expressions?

Answer 6

the slope is just the derivative
2 tan^2 (x) / cosx

umm..i always just use one..what u mean by 2 different expressions?

Answer 7

cuz i took the common denominator

Answer 8

evaluate your derivative at x=pi/3

Answer 9

I did, but i got a completely different answer than the book's answer
so i am thinking i might do the derivative wrong
can someone show me how to get the derivative

Answer 10

dy/dt = (sin(x)/cos^2(x))(2cos(x)^2+1)

Answer 11

Just wolfram it if you are checking your work
http://www.wolframalpha.com/input/?i=+1%2Fcosx+-+2cosx+derivative

Answer 12

what did you get when you put pi/3 into your derivative?

Answer 13

how u get (2cos(x)^2+1), and shouldnt it be a + between

Answer 14

\[y=\frac{1}{\cos(x)} -2\cos(x) ?\]

Answer 15

d/dt(1/cosx) = sin(x)/cos(x)^2 this is from the quotent rule
d/dt(-2cos(x) ) = 2sin(x)

Answer 16

is that your function? (the one @myininaya typed?) that's what i used.

Answer 17

yes

Answer 18

then add them together

Answer 19

\[y=\sec(x)-2\cos(x) => y'=\sec(x)\tan(x)+2\sin(x)\]

Answer 20

the answer can look 1000 different ways ....

Answer 21

yea, i did what myininaya shows , but i further took the common denominator ...so i guess i should not do it?

Answer 22

but there is only one slope at x=pi/3

Answer 23

no dont take the common den it will make it harder

Answer 24

just split it into two derivatives

Answer 25

d/dt(x+y) = dx/dt+dy/dt

Answer 26

ohh ..i will try to do the question again without spilting them together thankss

Answer 27

\[y'_{(\frac{\pi}{3},1)}=\sec(\frac{\pi}{3}) \tan(\frac{\pi}{3}) +2 \sin(\frac{\pi}{3})\]



So\[\cos(\frac{\pi}{3})=\frac{1}{2} ; \sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}\]

Answer 28

I think his problem is calculating the derivative

Answer 29

oh i thought he said he got what i got?

Answer 30

it is calculate the equation of the tangent

Answer 31

so the derivative is the slope
and solve for b
and then y and x..make it in standard form like that

Answer 32

you'll have to get the derivative first. and whether it is simplified or not, plugging in x=pi/3 into will give you the slope.

Answer 33

because that's all you need. you have a point, you have slope... put it in point slope form.

Answer 34

he knows all this, the question should of been "how do i take this derevative" i think

Answer 35

ok thanks everyone, i think i will know how to figure out the rest on my own
openstudy sucks that can only give out 1 medal :/

Answer 36

:)

Answer 37

lol

Answer 38

imaginary medals for everyone lol

Answer 39

thanks everyone!!!!!! so much so much !!! really dont know who to give lol
imaginery medals everyone! thanks