Question

If cosA = 1/2 with A in QIV find cos A/2

Answer 1

First you need to figure out what A is, any ideas?

Answer 2

Would it be 300 degrees?

Answer 3

Explain how you arrived at that conclusion for me please

Answer 4

If cos of A is 1/2 and in quadrant 4 on the unit circle shows 300... Am I off on thinking that way?

Answer 5

uhm, well let me show you how I think about it. (it is not 300) So in the 1st quad, which angle has a cosine of 1/2?

Answer 6

60

Answer 7

I apologize, I was incorrect. It is 300, but let's still say why

Answer 8

so if we graph,

Answer 9

Can you tell me the value of each side in terms of x?

Answer 10

and label however you choose for the angles

Answer 11

Not sure I follow

Answer 12

so you know how for 45 deg we get a 1, 1, √2 triangle, how about for the one with 60 deg

Answer 13

x, 2x, x sqrt 3

Answer 14

good so can you label those on our picture?

Answer 15

x= x, h= 2x, y= x sqrt 3

Answer 16

And what would be the value of angle z?

Answer 17

300

Answer 18

in regards to the y axis

Answer 19

30

Answer 20

ok so that is how we are going to draw A/2. You have determined that A is 300 now A/2=?

Answer 21

150

Answer 22

so can you graph that for me please

Answer 23

I'm on my iPad and it can't access the utilities

Answer 24

k draw it for yourself then

Answer 25

then tell me which quadrant it falls in and what angle is formed with the y axis

Answer 26

QII and 60 degrees

Answer 27

good, so now, can you figure out what the cosine value is?

Answer 28

-sqrt. 3/2 ?

Answer 29

yuppers, and why?

Answer 30

Idk because if I use the half angle formula I get sqrt of (3/4)...

Answer 31

well... you could use that, but it's a lot easier to just look at the pic. The reference angle will always be the one that is created by the original angle and the x axis

Answer 32

Think about how we labelled the sides before

Answer 33

use that to come to your conclusion for this new triangle

Answer 34

Well my prof wants to see that formula.. Is that answer I got right?

Answer 35

oh well, i didn't know that haha but tell me it again? you gave me two answers. Also you should learn this way it's a heck of a lot easier than remembering all of the formulas

Answer 36

Haha no worries. I got -sqrt of 3/4

Answer 37

yup that's it

Answer 38

I personally do it this way. I can't remember my name half the time so this def helps

Answer 39

Ha right on, thank you!

Answer 40

np have a good one