Question

find the exact value of tan22.5 using the half angle formula.

im at ((sqrt2)/(2))/((1+(sqrt2))/(2))

Answer 1

thats alot of (((())))) to keep track of :)

Answer 2

sorry!

Answer 3

sqrt(2)/2
-----------
1+sqrt(2)/2

is what youve got so far?

Answer 4

yesss

Answer 5

we can "cross out" the /2 parts since 1/2 over 1/2 = 1

sqrt(2)
--------
1+sqrt(2)

Answer 6

now to rationalize the bottom we need to divide by 1-sqrt(2) over 1-sqrt(2)

Answer 7

the conjugate? right?

Answer 8

thats correct, the conjugate...

Answer 9

thats correct, the conjugate...

Answer 10

sorry how do you know when you can multiply by that? is it because i have a + in between the two values on the bottom?

Answer 11

that right, when we have the denominator stuck together by addintion/subtraction, we need to use the conjugate.

Answer 12

and id for example i had 1 - sqrt(2) then i'd still use the opposite sign?

Answer 13

there are 3 things that can happen here:

we can multiply by the same value and get:

(a+b)(a+b) = (a^2 +2ab +b^2) which doesnt help us out.

(a-b)(a-b) = (a^2 -2ab +b^2) which is a bother as well

but,

(a+b)(a-b) = (a^2 - b^2) which is what will do it for us, so the conjugate is the same first and last, but a change in sign..

make sense?

Answer 14

ahhh i remember now! foiling. sorry im a junior in college taking precal and it's been three years since i saw any algebra so im extremely rusty. it's starting to come back

Answer 15

it was 20 years before I tried college :)

Answer 16

okay so now i used the conjugate and got sqrt(2)-2

Answer 17

thats your top part of the fraction i think

sqrt(2) times 1-sqrt(2) = sqrt(2) - 2

the bottom becomes:

1+sqrt(2) times 1- sqrt(2)

1 - 2 = -1

together we get:

sqrt(2) - 2
--------
-1

so we have a negative in this thing that needs to be dealt with

Answer 18

pretty much its:

-(sqrt(2)-2) = -sqrt(2)+2 = 2-sqrt(2) right?

Answer 19

right