Question

Find two values on the interval (0, 2pi) where the slope of the tangent to the graph of f(x)=cos(2x) is equal to square root of 3

Answer 1

take the derivative
set it equal to \(\sqrt3\)
solve for \(x\)

Answer 2

I found the derivative
f ' (x) =-2sin(2x)

Answer 3

I am stuck on solving for x

Answer 4

k that looks good

Answer 5

divide by \(-2\) then think
or appeal to the unit circle

Answer 6

\[-2\sin(2x)=\sqrt{3}\]
\[\sin(2x)=\frac{ \sqrt{3} }{ -2 }\]

Answer 7

right

Answer 8

what about the 2x?

Answer 9

should be familiar

Answer 10

you know a number where the sine is \(-\frac{\sqrt3}{2}\) ?

Answer 11

at 120 degrees or (2pi)3

Answer 12

i don't think so

Answer 13

you want to be in quadrant 3 or 4 because sine is negative

Answer 14

sorry, let me go look at a unit circle

Answer 15

k

Answer 16

use radians, not degrees
none of this works in degrees

Answer 17

let me know when you get \(\frac{4\pi}{3}\)

Answer 18

also \(\frac{5\pi}{3}\)

Answer 19

\[x =\frac{ 4\pi }{ 3 } \]
\[x=\frac{ 5\pi }{ 3}\]

Answer 20

ok good
but you have \(2x\) not \(x\)

Answer 21

sorry I had to look it up and type them
yes sorry and then I solve for x

Answer 22

so it should be \(2x=\frac{4\pi}{3}\iff x=\frac{4\pi}{6}=\frac{2\pi}{3}\)
in other words, divide by two

Answer 23

any hints so that I can recall this information without looking it up everytime, I only have the first quadrant memorize

Answer 24

and x = (5pi)/6

Answer 25

similarly
\[2x=\frac{5\pi}{3}\iff x=\frac{5\pi}{6}\] the solving for \(x\) part with \(2x\) is not supposed to be the hard part

Answer 26

true, sorry, I am a little slow

Answer 27

no hints, just visualize it
if sine is negative you are below the x axis, not above

Answer 28

a little slow? i doubt it
btw this is the first time i looked
"anne fibian" great!

Answer 29

Yes, old joke I found in a textbook

Answer 30

there is a great little exercise for collecting data and creating the sine and cosine graphs using a frog

Answer 31

?

Answer 32

just helps me remember where the sine graph begins

Answer 33

got it

Answer 34

just explaining why I use the username Precal and the frog "Anne Fibian"

Answer 35

Thanks so much, you give me hope that one day I too can conquer Calculus