Question

Given cos(x)= 2/3 , with 3pi/2 < x < 2pi, find cos (x/2), sin (x/2) , and tan (x/2)

Answer 1

Well, do you know where on the unit circle \(\frac{3\pi}{2} \lt x\lt 2\pi\) is?

Answer 2

that is 270 to 360

Answer 3

got it ,Q4.

Answer 4

So, another note, do you know your half angle formulas?

Answer 5

i dont know them by memory but i have them written down.

Answer 6

Can you type them here? Then I can cross check with you.

Answer 7

\[\sqrt{\frac{ 1+cosA }{ 2 }} is for Cos \]

Answer 8

well plus or minus in front

Answer 9

should we do that one first?

Answer 10

Sure thing

Answer 11

so for A would it be 2/6 plugged in?

Answer 12

I prefer writing it out in this fashion:\[\cos\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1+\cos(x)}{2}}\]

Answer 13

Yes, try that out, see what you get.

Answer 14

.99 and -.99

Answer 15

so would it be 1 and -1?

Answer 16

Oh, I forgot to ask you one thing, is cosine positive or negative in Q4?

Answer 17

oh positive

Answer 18

so it has to be 1

Answer 19

wait why didnt you put in "cos(2/6)" instead of "2/3"

Answer 20

or is that how you check the answer? sorry, i'm horrible at this. obviously.

Answer 21

ok restart

Answer 22

@_lostmathstudent what does cosine mean? what is it's definition?

Answer 23

you are right, it should have been 2/6

Answer 24

it's adjacent/hypotenuse

Answer 25

ok so cos(2/3) what is the adj and what is the hyp?

Answer 26

adj is 2 hyp is 3

Answer 27

so now picture time