Question

HELP ME FILL IN THE BLANK FOR THIS EQUATION!!
sin pi/4 sin pi/6 = 1/2 (cos pi/2 "blank" 5pi/12)

Answer 1

I know that you can simplify some of the trig points using the unit circle
sinpi/4=sqrt2/2
sinpi/6=1/2
cospi/2=0
so then (sqrt2/2)(1/2)=(1/2)(0) "blank" 5pi/12

Answer 2

uh...

Answer 3

\[(\sqrt2/2)(1/2)=(1/2)(0) "blank" 5\pi/12\]

Answer 4

Im not sure...

Answer 5

@malcolmmcswain @pooja195 @Jaynator495

Answer 6

basically we need a trig function that can fit into the blank to make both sides equal, but that is where I am stumped!

Answer 7

there is something wrong in your statement.
right hand side is zero but left hand side is not equal to zero.

Answer 8

she has left out the operation,
+"blank"

Answer 9

\[\sin (\frac{ \pi }{ 4 })\sin(\frac{ \pi }{ 6 })=\frac{ 1 }{ 2 }(\cos (\frac{ \pi }{ 2 })blank(\frac{ 5\pi }{ 12 })\]

Answer 10

is this it?

Answer 11

+blank
otherwise rhs is zero

Answer 12

simplifying like you began is probably best

Answer 13

cospi/2 can't be right it makes the entire right side = 0 and the left side does not equal that.

Answer 14

doesn't matter what trig function you put in for blank that zero will make the right side equal zero no matter what you do

Answer 15

shift evertything other than the blank to the left

convert \(5\pi/12\) to \(\pi/4 +\pi/6\)

use sin(A+B) formula and cos(A+B) formula and see what you get

Answer 16

\[\sin (\frac{ \pi }{ 4 })\sin(\frac{ \pi }{ 6 })=\frac{ 1 }{ 2 }(\cos (\frac{ \pi }{ 2 })+blank(\frac{ 5\pi }{ 12 })\]

Answer 17

OHHHHHHH

Answer 18

assume there is a plus before the blank, that is the only way its solvable

Answer 19

it's + blank

Answer 20

yea cuz otherwise it's an untrue statement

Answer 21

\[\sin (\frac{ \pi }{ 4 })\sin(\frac{ \pi }{ 6 })=\frac{ 1 }{ 2 }(\cos (\frac{ \pi }{ 2 })blank(\frac{ 3 \pi +2\pi }{ 12 })\]

Answer 22

i'd help but she's not on to double check the equation

Answer 23

\[\sin (\frac{ \pi }{ 4 })\sin(\frac{ \pi }{ 6 })=\frac{ 1 }{ 2 }(\cos (\frac{ \pi }{ 2 })+blank(\frac{ 3 \pi +2\pi }{ 12 })\]

Answer 24

simplify and get

blank(\(\frac{3\pi}{12}+\frac{2\pi}{12}\))=?

Answer 25

@cutiecomittee123

Answer 26

@baru sorrry I was cleaning my house up

Answer 27

okay I took another look at the origional equaion and yes it is minus, not addition
so it should be cos pi/2 - "blank" 5pi/12

Answer 28

@Ac3 Hey I am back on, if you still want to help, you are totally welcome.

Answer 29

we get
blank(5pi/12)=\(-1/\sqrt{2}\)

no trig function seems to solve this :(

Answer 30

shoot... well there has to be a solution @baru

Answer 31

technically the left side is equal to sqrt2/4
so the equation is
sqrt2/4 = 1/2 (cos (pi/12) -____5pi/12)

Answer 32

\[\sqrt2/4=1/2(\cos(\pi/12-____5\pi/12)\]

Answer 33

hey, its cos(pi/12),

everyone's been thinking its cos(pi/2), which is zero

Answer 34

then our equation becomes \[\sqrt2/4=1/2((1+\sqrt3)/(2(\sqrt2))-____5\pi/12\]

Answer 35

idk why it isnt presenting it correctly.

Answer 36

but i am still stuck :((((

Answer 37

@baru

Answer 38

0

Answer 39

what about 0?

Answer 40

+3x

Answer 41

3times

Answer 42

1/12*(24k+-3/12)=1/12*(6 ? 5)

Answer 43

k are integer

Answer 44

wait where is the 24k from?

Answer 45

cos(x)=sqrt(2)/2-> x= 2kpi+-pi/4

Answer 46

okay I am not seeing how that works?

Answer 47

Hey, can u use the equation Editor button and type out the question correctly.... Do double check, because it's unsolvable if u miss anything.... I have to leave now, but I'll have a go when I get back

Answer 48

And should consider closing this thread and opening a new one....it's too cluttered and will scare off anyone else who might have an answer

Answer 49

Tag me if u make a new one :)
Cya

Answer 50

\[R.H.S=\frac{ 1 }{ 2 }\left( \cos \frac{ \pi }{ 2 }Blank \frac{ 5 \pi }{ 12 } \right)=\frac{ 1 }{ 2 }\left( \cos \left( \frac{ \pi }{ 2 }\times \frac{ 6 }{ 5 \pi }\times \frac{ 5 \pi }{ 12 } \right) \right)\]
\[=\frac{ 1 }{ 2 }\cos \frac{ \pi }{ 4 }=\frac{ 1 }{ 2 }*\frac{ 1 }{ \sqrt{2} }\]