Question

General Identities
(in Trigonometry)
ADDITION AND SUBTRACTION IDENTITIES

FIND THE VALUE OF:

cos π/12

Answer 1

cos(π/12)=cos(π/4 - π/6)
and then you can use compound angle identities

Answer 2

or use
1/12= 1/3-1/4

Answer 3

the difference formula for cosine
\[\cos(\theta-\phi)=\cos\theta\cos\phi+\sin\theta\sin\phi\] (i still always have to look this up)

Answer 4

is cos π/12 = cos 15 degrees?

Answer 5

yes

Answer 6

yes, but that doesn't use the difference(subtraction) identity

if you use the difference formula then you will get the exact result (with square roots and such)

Answer 7

oh i see
how is this done then?
i dont get what you're saying above with all those fractions

Answer 8

cos(A - B) = cosAcosB + sinBsinA
cos(π/4 - π/6)=(cosπ/4)(cosπ/6) + (sinπ/4)(sinπ/6)
and then you can use special triangles or whichever way you were taught

Answer 9

The trick in this problem is to recognise the fraction 1/12 can be expressed as a difference of simpler fractions, (use either damoss, or my conversion)

then apply the difference formula, the trig identities of the simpler fraction are 'known', or can be found eaisly

Answer 10

why is it 1/3-1/4?
i dont get that?
@UnkleRhaukus

Answer 11

@damoss how did you get cos(π/4 - π/6)?

Answer 12

hm okay it may be easier for you if you're more comfortable with degrees to convert it to degrees. So π=180, yes? Then π/4=180/4=45 degrees and π/6=180/6=30 ; then 45 - 30=15

Answer 13

1/3-1/4 = 4/12 - 3/12 = 1/12

Answer 14

1/4 - 1/6 = 6/24 - 4/24 = 2/24 = 1/12

Answer 15

cos15=cos(45 - 30) if you will

Answer 16

(yeah it is a bit easier in degrees)

Answer 17

i see

Answer 18

will the answer be:
√(6)/4 - √(2)/4
?
@UnkleRhaukus @damoss

Answer 19

i believe that negative should be a positive

Answer 20

make sure you used the correct identity, cos(A - B) = cosAcosB + sinBsinA

Answer 21

√(6)/4 + √(2)/4
is that it already?
@damoss

Answer 22

yep

Answer 23

okay thanks :)

Answer 24

That is right, good work

but you can simplify a little bit further

√(2)/4 is a common factor

Answer 25

√(2)/4 (√(3) + 1 )

so is this the final answer?
@UnkleRhaukus

Answer 26

YES top stuff!

Answer 27

okay thanks @UnkleRhaukus