Question

sec (-pi/12) I'm doing sum and difference formulas and I don't know how to start this one. Will fan and medal

Answer 1

Which one

Answer 2

HI!!

Answer 3

you want to first find \(\cos(-\frac{\pi}{12})\) then flip it to get secant

Answer 4

if you are going to use the "difference formula" you first have to realize that \[\frac{1}{4}-\frac{1}{3}=-\frac{1}{12}\] so
\[\frac{\pi}{4}-\frac{\pi}{3}=-\frac{\pi}{12}\]

Answer 5

then use the formula to compute
\[\cos(\frac{\pi}{4}-\frac{\pi}{3})\]

Answer 6

you know the formula to use ?

Answer 7

Yes i do

Answer 8

@misty1212 I didnt get the answer that my book has

Answer 9

@amistre64 or @freckles sorry to bother you but do you know how to do this?

Answer 10

what did you end up with, misty explained it the same i would have

Answer 11

what is our difference formula for cosine?

Answer 12

I ended up with 1/4 (sqrt2+sqrt6)
The book says its sqrt 6-sqrt 2

Answer 13

sqrts can be a handful to 'rearrange'

lets see what we get

cos(a-b) = cosa cosb - sina sinb

cos(-pi/12) = cos(pi/4) cos(pi/3) - sin(pi/4) sin(pi/3)

cos(-pi/12) = sqrt(2)/2 1/2 - sqrt(2)/2 sqrt(3)/2

cos(-pi/12) = sqrt(2)/4 - sqrt(6)/4

sec(-pi/2) = 4/(sqrt(2)-sqrt(6))

this is what im getting so far ....

Answer 14

I thought there was a plus in the second part of the formula

Answer 15

.... good catch, there is.

so that just makes the bottom a + instead of a -

Answer 16

i was wondering how the conjugate was gonna turn out ... i feel better now

Answer 17

4
---------------
sqrt(2) + sqrt(6)





4 sqrt(2)-sqrt(6)
--------------- * -------------
sqrt(2) + sqrt(6) sqrt(2)-sqrt(6)




4(sqrt(2)-sqrt(6))
---------------
2 - 6




sqrt(6) - sqrt(2)

Answer 18

Why would I put the four on top?

Answer 19

because sec = 1/cos

Answer 20

if cos = a/b then sec = b/a

Answer 21

we found: cos = k/4 so sec = 4/k

Answer 22

Oh I got it

Answer 23

the conjugate (this familiar?) takes care of the simplification

Answer 24

Can you help me with one more?

Answer 25

not at the moment, need to attend to some real life issues on my end ....

Answer 26

Sorry, thanks for all the help :D