Question

In the Half Angle ID how do you know whether to use the + or - sign?

Answer 1

ID ?

Answer 2

anyone :c

Answer 3

identity.

Answer 4

Both signs.

Answer 5

half angle identity of what ?

Answer 6

\(\pm\) is just one addition that something applies to both signs.

Answer 7

yea but youd have to chose wether its - or +

Answer 8

You have to choose both. See, it's actually the point that a square root can be both positive and negative.

Answer 9

For example, the square root of 64 is \(\textbf{both}\) 8 and -8. If you're lazy, then you say that it is \(\pm 8\). Get the point?

Answer 10

where did half angle come in this picture ?

Answer 11

sin(x/2) and cos(x/2) @hartnn

Answer 12

Okay so like if you were to solve Cos (13pi/12 )

Answer 13

how do you know it simplifies to -\[-\sqrt{1+\cos (13\Pi/6)}/2\]

Answer 14

Like how do you decide theres a (-)

Answer 15

depending on the quadrant in which the angle lies.

Answer 16

13 pi/12 lies in which quadrant ?

Answer 17

1?

Answer 18

Because you have to mult by 1/2

Answer 19

13pi/12 = pi + pi/12 , right ?

Answer 20

you mean 1/2 times pi/ 13 ... Like thats how to simplify it

Answer 21

oops i mennt 1/2 times 13pi/6

Answer 22

before doing 1/2 times..... whatever,
u need to find where your original angle lies., in which quadrant.

Answer 23

oh

Answer 24

13pi/12 = pi+pi/12
lies in which quadrant ?

Answer 25

hint : 1st Quad : 0 to pi/2
2nd Quad : pi/2 to pi
3rd Quad : pi to 3pi/2

Answer 26

if would be Q2 but like how does 13pi/12 = pi+pi/12

Answer 27

pi + some angle will go beyond 2nd Quadrant
so its in 3rd Quadrant, ok ?

Answer 28

Oh okay

Answer 29

but still dont get how you did 13pi/12 = pi+pi/12

Answer 30

that is simple arithmetaic, since, 13pi/12 was greater than pi, i subtracted pi.
and got pi/12
so, 13pi/12 = pi+pi/12

Answer 31

and in 3rd Quadrant, cosine is negative...
hence, you select, - **minus**

Answer 32

Lol okayyes can you give me another problem so I can practice how to find with Q its in

Answer 33

yes,
13pi/7
which Quad ?

Answer 34

wuld it also be in Q 3...

Answer 35

nopes, how Q 3 ?

Answer 36

I thought of it like pi + pi/7

Answer 37

can you convert radians into degrees ?

Answer 38

man hhow come I dont understand how to do it x_x

Answer 39

oh yes

Answer 40

i will give a better method,
can you convert radians into degrees ?
then convert and tell me what u get.

Answer 41

Wait would it be in the Q2

Answer 42

no.

Answer 43

13pi/7 = 13*180/7 = 334.28...now 334 is in which Q ?

Answer 44

its less than 360 and > 270

Answer 45

the 4th ._.

Answer 46

yup.
so convert the angle into degrees and then its easy...

Answer 47

one more ?

Answer 48

7pi/6 ?

Answer 49

yes

Answer 50

okay so I would use the method part / whole

Answer 51

so 7pi/6 / 2pi = x / 360

Answer 52

?
pi radians = 180 degrees
7*180/6 =210
210 in which Quadrant ?

Answer 53

I got the Q3

Answer 54

yes.
got it how to find which Q ?

Answer 55

wait one more lol

Answer 56

ok, 3pi/4

Answer 57

lol I alreadyady know that one its in Q2

Answer 58

lol
then pi/12

Answer 59

Q1

Answer 60

yes, last
5pi/3

Answer 61

oh srry I am also doing my essay lol but um okay for thisone it will beeee

Answer 62

um so it would be in Q2

Answer 63

no, try again.

Answer 64

WAIT I MEANT Q$

Answer 65

*Q4

Answer 66

excellent!
now i award you Masters Degree in finding Quadrant of an angle. :P
you can continue with your essay....

Answer 67

lol thnkx btu I have more math questions.. I hve a test today x_x

Answer 68

\[ \begin{array}l\color{red}{\text{w}}\color{orange}{\text{e}}\color{#e6e600}{\text{l}}\color{green}{\text{c}}\color{blue}{\text{o}}\color{purple}{\text{m}}\color{purple}{\text{e}}\color{red}{\text{ }}\color{orange}{\text{^}}\color{#e6e600}{\text{_}}\color{green}{\text{^}}\color{blue}{\text{}}\end{array} \]
sure, do ask...

Answer 69

okay I'll make new questions

Answer 70

:)