Question

what is tan(pi/8) rounded to 4 decimal places
what is tan(pi/8) rounded to 4 decimal places
@Mathematics

Answer 1

pls show work

Answer 2

\(\sqrt{2}-1\) Do they want you to use any special means to compute the square root of two?

Answer 3

they just say find the value rounded to 4 decimal places

Answer 4

plug it into your calculator. then round it

Answer 5

So you can use the tangent half-angle formula here... pi/8 is just one half of pi/4.

Here is the diagram for the tangent half-angle formula: http://en.wikipedia.org/wiki/File:Weierstrass_substitution.png

Answer 6

ok what about eyust method...can i actually do that

Answer 7

it's up to your instructor

Answer 8

bsed on the stuff we were doing earlier than they probably are just tryoing to teach you how to use your calc in this case

Answer 9

ok what if i have sec(97) theres no button for sec on the calc...what do i do then

Answer 10

well sec x = 1/cos x

Answer 11

i could show you why if you would like

Answer 12

but thats a property you should memorize

Answer 13

yea pls go ahead

Answer 14

honestly i cant quite remember.. it has to do with the properties of the unit circle.. your teacher may have derived it.. maybe mathteacher can show you?

Answer 15

mathteacher are you there?

Answer 16

Yes I'm still here sorry.

Answer 17

but for now just memorize these:

http://www.mathacademy.com/pr/prime/articles/trig_ident/trig_ident_6.gif

Answer 18

why does secx = 1/cosx?

Answer 19

eyust -- that is just a definition. It is defined to be that way.

Answer 20

using that definition, mathteacher, how can i solve sec(97)

Answer 21

sec(97) = 1/cos(97)

Answer 22

You wouldn't "solve" it, you would "evaluate" it. And since 97 is not a "nice" angle (pi/2, pi/3, or some combination of those), then we just use a calc, or some more advanced numerical approximations.

Answer 23

so our final evaluation would just be 1/cos(97)?

Answer 24

yep

Answer 25

is that 97 in degrees or radians?

Answer 26

degrees

Answer 27

make sure your calc is set to degrees when you type it in

Answer 28

o ok...when i type it in i get -8.205509...4 decimals would be -8.2055...thats it?

Answer 29

mathteacher,is that it?