Question

What is the slope of the tangent line to the graph of y= tan^2x at x = pi/4

Answer 1

4

Answer 2

So the slope of the tangent line is the derivative of the function.

Answer 3

yup, got that. then plug in pi/4

Answer 4

I assume that is where the unit circle comes into play

Answer 5

y' = [(tanx)^2]' = 2 * (tanx) * (Sec^2x) yeah and now just plug in pi/4

Answer 6

which is what I would like an explanation of pls!

Answer 7

driving me up the wall

Answer 8

what exactly is it saying when the equation is tan(pi/4)?

Answer 9

Okay so you want the slope when x = pi/4
you are given an equation: y = tan^2(x)
y' = 2 * tanx * Sec^2(x)
y' ( pi/4) = 2 * tan (pi/4) * Sec^2(pi/4)

Answer 10

all good with that - thanks

Answer 11

then what?

Answer 12

it"s calculating what tan (pi/4) is that is bothering me

Answer 13

or sec (pi/4)

Answer 14

oh lol tan (pi/4) = Sin (pi/4) / Cos (pi/4)
Sec (pi/4) = 1 / Cos (pi/4)

Answer 15

yup broke it down to that

Answer 16

where do locate pi/4 though?

Answer 17

Now plug in: Sin (pi/4) = sqrt(2)/2
Cos (pi/4) = sqrt(2)/2

Answer 18

pi/4 is in radians, pi = 180 degrees

Answer 19

pi / 4 radians= 180 / 4 = 45 degrees

Answer 20

I used the unit circle to get the points - but, do I need to memorize this by heart?

Answer 21

oh sweet! that really helped!

Answer 22

okay glad i helped..

Answer 23

one sec

Answer 24

:-)

Answer 25

I see how you got the degrees, my issue is how shld I know that at that point of 45 degrees that sqrt2/2 is the point?

Answer 26

I know pull the x value for cos and the y value for sin,

Answer 27

but, do I need to memorize that at 45 degrees the corresponding point is (sqrt2/2, sqrt2/2)?

Answer 28

No no, when you get this:
y' = 2 * tanx * Sec^2(x)
plug in pi/4 wherever you see x

Answer 29

and then you wull get the point

Answer 30

my problem is that we are not allowed calculators in the exam

Answer 31

hence, my rather ridiculous question

Answer 32

okay then you will have to memorize Sin and Cos values of:
0, pi/6, pi/4, pi/3, pi/2, pi

Answer 33

ok, cool! can I also use pythagoras theorem?

Answer 34

yea why not

Answer 35

ok cool