Question

Help finding the exact value of this with no calculators? Step-by-step? Will give medal & fan.
tan(17pi/12)

Answer 1

well pi =180 degree
if you didnt know

Answer 2

so put that value of pi in there
you get tan(255)
which can be written as tan(180+75)
=tan75=tan(30+45) = tan30+tan45/1-tan30tan45
sow put the values of tan30 and tan45 and find the answer

Answer 3

I don't know how to get tan from anything without using a calculator...

Answer 4

o_o

Answer 5

http://www.trigonometry-help.net/img/trig-tables_clip_image018.gif

Answer 6

memorise this table pls
it is important

Answer 7

Oh okay, thank you

Answer 8

@ganeshie8 sorry if you are busy,i am kinda sleepy,can u pls explain this final step to her ^^

Answer 9

though there is hardly anything to explain

Answer 10

still @TammisaurusRex you should memorise that table

Answer 11

and those formula like
tan(A+B) = tanA+tanB/1-tanAtanB

Answer 12

good !

Answer 13

I'm writing that table down now. What do I do after I get tan(30) = 1/sqrt3 and tan(45) = 1?

Answer 14

Do I just add them?

Answer 15

@ganeshie8

Answer 16

Would it be tan(30 + 45) = tan(30) + tan(45) / 1 - tan(30)tan(45) ?

Answer 17

So (1/sqrt3) + 1 / 1 - (1/sqrt3)(1)
(1/sqrt3) + 1 / 1 - (1/sqrt3) ?

Answer 18

I just am not really sure how to add or subtract with 1/sqrt3 without a calculator...

Answer 19

\(\large \tan(30+45) = \dfrac{\tan 30 + \tan 45}{1- \tan 30 ~\tan 45} = \dfrac{\frac{1}{\sqrt{3}} + 1}{1 - \frac{1}{\sqrt{3}}}\)

Answer 20

multiply top and bottom by sqrt(3)

Answer 21

\(\large \dfrac{\frac{1}{\sqrt{3}} + 1}{1 - \frac{1}{\sqrt{3}}} = \dfrac{1+\sqrt{3}}{\sqrt{3} - 1}\)

Answer 22

rationalize the denominator

Answer 23

\(\large \dfrac{1+\sqrt{3}}{\sqrt{3} - 1} \times \dfrac{\sqrt{3} + 1}{\sqrt{3} + 1} = \dfrac{(\sqrt{3}+1)^2}{3-1} = \dfrac{3+2\sqrt{3} + 1}{2} = 2+\sqrt{3}\)

Answer 24

Is that the exact answer?

Answer 25

yep !

http://www.wolframalpha.com/input/?i=tan%2817pi%2F12%29

Answer 26

thank you very much!

Answer 27

yw