Question

find an equation of the tangent to the curve at the given point. f(x)= 2sinx+3 at x=pi/6

Answer 1

A tangent is a straight line. Therefore, the equation of a tangent can be written in the form y= mx +c
where m=slope of the tangent
c= y-intercept of the tangent

Answer 2

to find the slope of the tangent at the point x=pi/6..
\[\frac{ dy }{ dx } (x=\frac{ \pi }{ 6 })\]

Answer 3

do you get up to that point??

Answer 4

yes

Answer 5

I plugged pi/6 on for all x

Answer 6

yes....that is correct!

Answer 7

then what do i do

Answer 8

f(pi/6)=4

Answer 9

that step is correct. you found the corresponding y-coordinate of the given x-coordinate (pi/6)

Answer 10

y-4=m(x-pi/6) ??

Answer 11

so now we can plug them in the equation y= mx +c to find the value of c.
y=4
x=pi/6
m=sqrt of 3

Answer 12

is that what you got for your value of the slope (m)??

Answer 13

how do you get m=sqrt of 3??

Answer 14

I differentiated the equation of the curve and replaced x with pi/6

Answer 15

what did you get for the slope??

Answer 16

im confused

Answer 17

can you show me how you got m=sqrt of 3

Answer 18

4=sqrt3(pi/6)+c ??

Answer 19

you would have to know the basic differentials...
\[y = \sin x \] \[\frac{ dy }{ dx } = \cos x\]

\[y = \cos x \] \[\frac{ dy }{ dx } = - \sin x\]

\[y = \tan x\] \[\frac{ dy }{ dx } = \sec ^{2}x\]

Answer 20

yes..

Answer 21

ok

Answer 22

are you ok with how i got the sqrt 3??

Answer 23

no

Answer 24

you can post that as a question because i use a shortcut method which i suppose would not be good for you....

Answer 25

ok so you replaced sin x with cos x which is sqrt of 3/2

Answer 26

yes....and you would have to know that if you differentiate a constant standing on its own you get zero...

Answer 27

yes i understand

Answer 28

ok....but i advice you would have to work on it...(on the topic differentiation)

Answer 29

so what does c equal

Answer 30

so have you found c??

Answer 31

y-4=sqrt3(x-pi/6)

Answer 32

if i have 4=sqrt3/6+c

Answer 33

no.....
\[4 = \sqrt{3} (\frac{ \pi }{ 6 }) + c\]

Answer 34

so you subtract 4-sqrt3(pi/6)

Answer 35

yes...

Answer 36

are you supposed to leave your values in exact form or in decimals???

Answer 37

exact form

Answer 38

so what did you get as the value of c??

Answer 39

3

Answer 40

that would be a decimal