Question

Evaluate 2sin(pi/3)cos(pi/3)

Answer 1

@jim_thompson5910 Hii are you busy? Up for any IB SL Math questions tonight?

Answer 2

you could use unit circle to evaluate both sin(pi/3) and cos(pi/3)

Answer 3

you could also use the double angle identity
and use unit circle once

Answer 4

Yes, I have it in front of me but I'm confused on what to do

Answer 5

can you find pi/3 on the unit circle?

Answer 6

yea it's 60 degrees right?

Answer 7

there should be an ordered pair designated to it

Answer 8

(x,y)=(cos(),sin())

Answer 9

1/2, sqrt3/2

Answer 10

so that means the cos(pi/3) is 1/2
and sin(pi/3) is sqrt(3)/2
plug in

Answer 11

ok gimme a sec

Answer 12

ok, just for clarification, what exactly am I doing once I plug them in? I mean am I just dividing, multiplying, etc? By the way, the answer in the back is (0.766, -0.643)

Answer 13

uhh hello..?

Answer 14

2sin(pi/3)cos(pi/3)
is multiplication

Answer 15

abc means a times b times c

Answer 16

Ohh ok my bad. so i got .037

Answer 17

how did you get that?

Answer 18

I just plugged into my calculator 2sin(pi/3) * cos(pi/3)

Answer 19

its not right, i know ;-;

Answer 20

sin(pi/3) is sqrt(3)/2 so replace sin(pi/3) with sqrt(3)/2
cos(pi/3) is 1/2 so replace cos(pi/3) with 1/2

\[2[\sin(\frac{\pi}{3})][\sin(\frac{\pi}{3})] \\ 2[ \frac{\sqrt{3}}{2}][\frac{1}{2}] = \frac{2}{2} [\sqrt{3}][\frac{1}{2}]=....\]
you can simplify a little

Answer 21

oops one of those sin were suppose to read cos

Answer 22

the second one right?

Answer 23

\[2[\sin(\frac{\pi}{3})][\cos(\frac{\pi}{3})] \\ 2[ \frac{\sqrt{3}}{2}][\frac{1}{2}] = \frac{2}{2} [\sqrt{3}][\frac{1}{2}]=....\]

Answer 24

ahh ok so did you get rid of the 2 in the beginning and then add in the 2/2 as a separate thing?

Answer 25

multiplication is commutative ab =ba

Answer 26

\[2 \cdot \frac{\sqrt{3}}{2} \cdot \frac{1}{2} \\ =\frac{2}{1} \cdot \frac{\sqrt{3}}{2} \cdot \frac{1}{2} \\ =\frac{2 }{2 } \cdot \frac{\sqrt{3}}{1} \cdot \frac{1}{2}\]

Answer 27

gotcha. But at any rate, I ended up getting 4.71

Answer 28

which, again, doesn't seem right since the answer in the back of the book is totally different

Answer 29

you do know 2/2=?

Answer 30

1

Answer 31

right so you have
\[\sqrt{3} \cdot \frac{1}{2} \text{ which is just } \frac{\sqrt{3}}{2}\]
I don't see how you are getting a number bigger than 1 ...

Answer 32

since sqrt(3)/2 is definitely less than 1

Answer 33

i think it's just cos im plugging it into my scientific calc then

Answer 34

ok

Answer 35

oh wait im so dumb i was doing pi3

Answer 36

im so sorry my bad

Answer 37

its .866 right

Answer 38

yes sqrt(3)/2 is approximately .866

Answer 39

yeah

Answer 40

ok but the answer says it's .766, -0.643

Answer 41

@brriiarr the fact that it shows two answers, when it should be one answer, suggests that maybe there's a mixup between the problem and answer

Answer 42

I don't know what your book is talking about the answer is sqrt(3)/2 which could be written approximately as .866

Answer 43

maybe it's a typo for .766 ???

Answer 44

Ah yes, sometimes there are typos in book. No book is published perfectly. sigh

Answer 45

crap ok. it says in a weird little font next to it sqrt3/2 but i guess you guys were right. umm..do you think i could ask for help on one more?

Answer 46

you might also want to check the question you type was the question you meant
and the answer that correspond to the question you asked was the right correspondence you chose

Answer 47

i think it really was just a typo :p

Answer 48

um but yea I have on more i needed a little help on

Answer 49

ok lol so it's just to find the perimeter and area of the sector. I'll draw it

Answer 50

rty

Answer 51

ahh so yea, i dunno how to do this at all