Question

plzzzz helppp: what is a positive value of tan1/2x when sin x=0.8?

Answer 1

@mossyfish plz helpp

Answer 2

any1 plz help if u no

Answer 3

@Hero

Answer 4

\[sinx=0.8\]
\[cosx=\pm \sqrt{(1-0.8^2)}=\pm0.6\]
\[\tan(x/2)=1-cosx)/sinx\]

Can you figure this out from here?

Answer 5

r u using the quadratic formula??

Answer 6

@mossyfish

Answer 7

Nope, trigonometric properties.

What are your answer choices, btw?

Answer 8

what is the trigonometric property? canu write it?

Answer 9

choic are: 0.5 0.4 0.33 0.25

Answer 10

if sin(x)=8/10=4/5
then we can find cos(x) by using the right triangle associated with 4/5.

Recall
\[\cos^2(x/2)=\frac{1}{2}(1+\cos(x)) \text{ and } \sin^2(x/2)=\frac{1}{2}(1-\cos(x))\]

so \[\tan(x/2)=\sqrt{\frac{1+\cos(x)}{1-\cos(x)}}\]

so basically you are given sin(x)=4/5
just find what cos is off of your right triangle you drew for sin(x)=4/5

Answer 11

how did u gt sin(x)=8/10=4/5??

Answer 12

that is what is given

Answer 13

you are given sin(x)=8/10

Answer 14

no its n the problem is: what is a positive value of tan1/2x when sin x=0.8?

Answer 15

right sin(x)=8/10

Answer 16

0.8 is same at 8/10?

Answer 17

of course

Answer 18

its nt 4/5?

Answer 19

8/10=4/5

Answer 20

it is called reducing a fraction

Answer 21

.8=4/5

Answer 22

ohh I see

Answer 23

ok now I don't gt where ur gttin the rest frm?

Answer 24

trig identities

Answer 25

http://www.purplemath.com/modules/idents.htm

Answer 26

oh now im gona use these identities to solve the problem?

Answer 27

half angle identities

Answer 28

ok how do I know which identity im gona use for this problem?

Answer 29

well the key is noticing it is asking for tan(x/2)
that looks like half an angle there
because of the over 2 part
so we know to use the half angle identity

Answer 30

so we gona use the tan(x/2)=1+cos x/1-cos x?

Answer 31

@myininaya

Answer 32

no
you can use
\[\tan(x/2)=\sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\]

Answer 33

so now I need to plug in?

Answer 34

@myininaya

Answer 35

after you find the value for cos

Answer 36

you know sin(x)=4/5

Answer 37

so what is cos(x)=

Answer 38

ugh can we plz go thro every step? how did we find the value of cos?

Answer 39

try to draw a right triangle for sin(x)=4/5
then find the adjacent side
brb

Answer 40

ok waitng

Answer 41

@mossyfish

Answer 42

I think @myininaya is doing a fine job helping you :) Tag me in other questions you might need help with.

Answer 43

she is but she said brb and I thought maybr u could help me for now...

Answer 44

ik shes helping me good

Answer 45

Okay well, continuing from where I was from..
When cosx=-0.6
tan(x/2)=(1+06)/0.8-2

When cosx=.6
tan(x/2)=(1-0.6)/0.8 which equals...?

Answer 46

u both are doin 2 diff things and its confusing me I need u to plz tel step by step if u culd?

Answer 47

Yeah this is why @myininaya should help you... We both have different methods of solving this, jumping back and forth between us isn't going to help you :( Good luck!

Answer 48

ok fine thnks

Answer 49

Have you drew a right triangle and use the sin(x)=4/5 to label the triangle yet?

Answer 50

yes

Answer 51

then find the missing side

Answer 52

which is what?

Answer 53

do I use the pathagreom theorem?

Answer 54

yep
it is a right triangle so use that theorem