Question

Give the solution of the equation in both exact form and decimal form (rounded to 3 decimal places!).

1=81tan(6x+5)-8

Exact Form:_____

Decimal Form:_____

Am I starting it correctly?
1=81tan(6x+5)-8
add 8 to both sides
9=81tan(6x+5)
divide both sides by 81
1/9=tan(6x+5)

from here, I'm not too sure how to continue :/ thanks!!

Answer 1

so far so good yes

exact is to undo the tan with the inverse tan function

Answer 2

so 1/9=arctan(6x+5) ? :/

wait just wanna make sure haha arctan=tan^-1 right?

Answer 3

tan' is a simple way to type it but yeah arctan= tan'

1/9 = tan(a) , tan' both sides

tan'(1/9) = a ; the rest is simple algebra moves

Answer 4

so now i plug in right?

do i plug in for the values where theres an x?

Answer 5

if so, it'd be like this?

1/9=tan(6x+5)

1/9=(6(arctan(1/9))+5) ?

or is it something else?

Answer 6

1/9=tan(6x+5)

tan'(1/9) = tan'(tan(6x+5))

tan'(1/9) = 6x+5 , continue to solve for x

Answer 7

ohh okay

arctan(1/9)-5=6x

(arctan(1/9)-5) / 6 = x ?

would that be the exact form? :/

Answer 8

that is the exact form yes

Answer 9

x= -0.81489

so x is about -0.815 ?

Answer 10

maybe, i dont have my calc with me :)

Answer 11

looks fine tho

Answer 12

haha okie :P

i just put tan^-1 (1/9) - 5 and then divided it by 6 hehe :)

Answer 13

okie yay thanks :)

Answer 14

yep