Question

okay what the heck am i supposed to do here! cos beta= -.82; 180 degrees< beta<270 degrees

Answer 1

I is supposed to solve the equation how do I do that?

Answer 2

even u getting beta value as 145.08 degrees from calculator?

Answer 3

umm please give me a second

Answer 4

no i got 0.999897589371505 but i just typed it in normal how do you do beta value?

Answer 5

cos ^-1 of -0.82
if u get in radians, convert in degree

Answer 6

why cos-1?

Answer 7

no u should do cos inverse
as cos beta =-0.82
beta = arccos (-0.82) or cos^-1 (-0.82)

Answer 8

i'm still not that good with inverseing why do we do that for?

Answer 9

if
\(sin x=\theta\)
then \(\theta = sin^{-1}x\)

Answer 10

to get the angle.

Answer 11

please hold i need to re check my calc

Answer 12

okay so now i soo how you got 145.08 degrees what is it for?

Answer 13

i used calculator
what u got when u used calculator?

Answer 14

same i just want to know what we do with it now cuz it's supposed to be > 180 and < 270

Answer 15

okk,
we use this
cos(360-theta)=cos theta
put theta=145.08 here

Answer 16

ok so 360-145.08=214.92 is that it?

Answer 17

yup thats your required angle.

Answer 18

so just to be clear we subtract theta from 360 because 360 is like the circle and theta is like the piece missiing from it so we get the degree of wha'ts left as our answer yes?

Answer 19

u can say that.....
but be careful with sine
sin(360-x)=- sin x
sin(-x)=-sin x
cos(-x)=cos x
cos(360-x)=cos x

Answer 20

as 0 degree corresponds to 360 degree

Answer 21

so does tan(360-x)=tan x?

Answer 22

its -tan x
because tan x = sin x/cos x

Answer 23

tan(360+x)=tan x
tan(-x)=-tan x
So
tan(360-x)=tan(-x+360)=tan(-x)=-tan x

Answer 24

wait i think i remember something like this so tan=sin/cos
and you inverse sin and cos right?

Answer 25

inverse sin and cos? why?to do what?

Answer 26

no like if it say sin beta=x then you do sin^-1x
and ummm.... idk bout cos

Answer 27

yes, for any ratio u can take inverse
if tan beta= x
beta = arctan x
if cos beta=y
beta = arccos y

Answer 28

awesomeness i think i get it but lets check

Answer 29

tan beta= -5.3;90 degrees < beta < 180 so i do tan^-1(-5.3) yes?

Answer 30

yup,do it

Answer 31

okay please hold

Answer 32

i got –79.31 so now i just subtract that from 360 and..... okay i got 439.31 and I know that can't be right... help?

Answer 33

but u can't use 360 with tan
because it becomes negative
tan(360-x)=-tan x
here u use 180
as tan's periodicity is 180
tan(180+x)=tan x
now put x=-79.31
and tell me what u get

Answer 34

i got 100.69!

Answer 35

that is so correct :)

Answer 36

if u want to verify
tan 100.69=-5.3

Answer 37

so i apologize but why is tan 180 instead of 360 because the other two are

Answer 38

because of the periodicity
sine and cos have 360 degrees as periodicity
means values for sin and cos repeat after 360
sin(x)=sin(x+360)
cos(x)=cos(x+360)
whereas tan has periodicity of 180
all tan values repeat after 180 degrees
tan(180+x)= tan x

Answer 39

oh does this has anything to do with the unit circle?

Answer 40

yup,thats related
http://en.wikipedia.org/wiki/File:Unit_circle_angles_color.svg
u can see graph of tan here:
http://en.wikipedia.org/wiki/File:Tan(theta).jpg

Answer 41

cool i got it thank you and have a good night ^-^

Answer 42

welcome :)
i'll have good evening here.