Question

cos(19pi/12) how would you find the exact value of this?

Answer 1

http://openstudy.com/study#/updates/51c3bd95e4b069eb00c4dbb3 I was looking at that, but I don't understand the half formula.

Answer 2

@precal
can you help me understand it please?

Answer 3

@tHe_FiZiCx99

Answer 4

@abb0t thank you for the help :)

Answer 5

._.

Answer 6

You're very welcome, @lolabieber make sure to fan + medal those who help.

Answer 7

Alright :)

Answer 8

cos(285 degrees)

Answer 9

do you have to use a particular method?

Answer 10

Yes I have formulas and the unit circle

Answer 11

ok but are you suppose to use sum and difference?
btw do you know how to convert it into degrees?

Answer 12

Yes those the sum and difference of tan, sin, or cos
And no I don't

Answer 13

I do if the radian is on the unit circle, but not if it's not

Answer 14

ok real quick pi is 180 degrees so
(19 times 180)=3420
divide that by 12 and you get 285 degrees

Answer 15

On the unit circle, 285 degrees is not listed so we have to find 2 angles that we know see if you can find two angles that you can add or subtract to create 285 degrees

Answer 16

\[\cos \frac{ 19 \pi }{ 12 }=\cos \left( \pi+\frac{ 7 \pi }{ 12} \right)=-\cos \frac{ 7 \pi }{ 12 }=-\cos \left( \frac{ 4 \pi+3 \pi }{ 12 } \right)\]
\[=-\cos \left( \frac{ \pi }{ 3 } +\frac{ \pi }{ 4 }\right)=?\]

Answer 17

so in order to convert it into degrees you always multiply by 180?

Answer 18

no pi is 180 degrees

Answer 19

yes but why did you multiply it

Answer 20

i think i get it a bit because its asking for 19 pis right? instead of just 1 pi?

Answer 21

all I really did was substitute the fact that pi is 180 degrees into the fraction and converted radians to degrees

Answer 22

no can you find two numbers from the unit circle that will give me 285 degrees

Answer 23

so it's between 3pi/2 and 5pi/3 so can one of them be 4pi/3

Answer 24

@surjithayer is using a reference angle

Answer 25

what do you mean?

Answer 26

no you are looking for 200 + 85 or 180 + 105 or something like that
you need to find two angles from your unit circle to create 285 degrees

Answer 27

forget the reference angle approach, it seems you have not covered reference angles yet

Answer 28

how about 330-45?

Answer 29

11pi/6 and pi/4

Answer 30

cos(330-45)=cos330cos45+sin330sin45

Answer 31

yes rewrite it in terms of pi as you stated above

Answer 32

then sub values and evaluate it

Answer 33

so it's cos(11pi/6 -pi/4)=cos11pi/6*cos pi/4-sin11pi/6*sin pi/4

Answer 34

yes

Answer 35

okay im going to solve it give me a minute

Answer 36

take your time

Answer 37

im not getting it im getting 11pi^2/24 - 11pi^2/24 and that's 0

Answer 38

I need to work it out, give me a moment

Answer 39

okay

Answer 40

cos(330-45)=cos330cos45+sin330sin45
\[\left( \frac{ \sqrt{3} }{ 2 } \right)\left( \frac{ \sqrt{2} }{ 2 } \right)+\left( \frac{ -1}{ 2 } \right)\left( \frac{ \sqrt{2} }{ 2 } \right)\]

Answer 41

is this what you substituted into your formula?

Answer 42

ohhhh okay I got confused wait let me try it again

Answer 43

why'd you use sqrt2/2 ?

Answer 44

never mind i figured it out

Answer 45

i got sqrt6 -sqrt2 over 4