Question

Solve for both exact form and decimal form (rounded to 3 decimal places). :)

1= 14tan (6x+8) - 1

not sure... but do I do this?

1= 14tan(6x) + 14tan(8) -1

add 1 to both sides

2=14tan(6x) + 14tan(8)

?? :/ is that the correct way to start? :/ thankyouu:)

Answer 1

no :D
1= 14tan (6x+8) - 1 /+1
2=14tan(6x+8) /14
1/7=tan(6x+8)

Let t=6x+8
1/7=tan(t), solve simple equation per t and then you are solving linear equation t=somethin+k*pi
something+k*pi=6x+8
-8+(something+k*pi)/6=x

Answer 2

tan( stuff) are complicated

Answer 3

ohh okay...

i'm not sure what you mean by the t=something + k*pi part though..

i know the k is the constant right? :/ but how do we figure out the something ?

Answer 4

1/7=tan(6x+8)

Let t=6x+8

1/7=tan(t)
t=arctan(1/7) (type on calculator -> t=0.1419+kPi, k is integer
0.1419+kPi=6x+8
-8+(0.1419+kPi)/6=x

you can simplify this if you want to :)

Answer 5

the tangent repeats every pi radians (every 180 deg)
once you find an answer, you can add pi to it to get another answer
(or subtract pi)
in fact you can add any multiple of pi to get another answer.

Answer 6

1= 14tan (6x+8) - 1

1= 14tan(6x) + 14tan(8) -1

can't do this. Tan(a + b) does NOT equal tana + tanb. Same applies to sin and cos

Answer 7

@purger -7.97635 + kπ/6 = x ?

not sure if that's right haha :P

and ohh okay @agent0smith oops :P

Answer 8

@iheartfood
6x+8=0.14189+kpi
6x=-7.85...+kPi
x=-1.309683+kPi/6, k is integer

Answer 9

ohh okay..

so does that simplify any further?

or is that what would be considered the exact form? :/ or is that the decimal form (since it's a reallyyyy long number haha) ?

Answer 10

If you needed exact form, which is odd in this case, just leave it as

6x+8 = tan^-1(1/7)

and solve from there, same as above..

Answer 11

so what id be solving for would result in the decimal form? :/

Answer 12

6x+8 = tan^-1(1/7)

solve for x:

x = (tan^-1(1/7) - 8)/6

Answer 13

No that's exact form, left as that.

Answer 14

x=0.216837257 ?

Answer 15

ohh so this is the exact form?

6x+8 = tan^-1(1/7)

Answer 16

See exact form above :P

Answer 17

oh.. so this is the exact form?

x = (tan^-1(1/7) - 8)/6

and this is the decimal form ?

x=0.217

?

Answer 18

x=-1.309683+kPi/6, k is the exact form, from @purger

Answer 19

be sure to be in radian mode

Answer 20

and round to 3 decimal places

Answer 21

forgot the kpi too

x = (tan^-1(1/7) - 8 + k*pi)/6

Answer 22

ohh okay :P was in the wrong mode :P

so exact form: x = (tan^-1(1/7) - 8 + k*pi)/6

and decimal form: -1.310

?? is that right now? :)

Answer 23

^decimal form needs kpi/6 too

Answer 24

ohh :/

so decimal form= -1310kpi
____________
6

??

Answer 25

is that how it's written? or is it -1.310(kπ/6) ?

and oops i forgot the decimal point above.. haha it should be -1.310 :P

Answer 26

PLUS kpi/6 :P

Answer 27

ohh ok :) yay! thank you!!! :)