Question

solve the equation 2tanC-3=3 tan C-4 algebraically for all values of C in the interval 0 12 years ago

Answer 1

Let me see whether I'm reading your problem statement correctly. Is this right?\[2*\tan(c-3) = 3*\tan (c-4)\]

Answer 2

\[2 \tan C-3=3 \tan C-4\] thts exactly the way its written in my paper

Answer 3

\[0 \le C < 360\]

Answer 4

\[0 \le C < 360\]

Answer 5

hello?

Answer 6

Knowing this helps a LOT.

Where you have \(2 \tan C-3=3 \tan C-4\) please substitute x for "tan C" because this simplifies the solution of the problem. Mind writing that out?

Answer 7

I got 2tan c=3tan c-1

Answer 8

I'd just made a suggestion that I'd thought might simplify the problem solution for you.

If you take my suggestion, you'd get 2x=3x-1.
Would you mind solving that for x?

Answer 9

(Remember that this x represents tan C.)

Answer 10

If

2x=3x-1, please add 1 to both sides and simplify the result.

Answer 11

oh so I got -tan c=-1?

Answer 12

or -1=x

Answer 13

?

Answer 14

My result is x=1. Would you please check your work? However, your tan C = 1 is correct.
Are you able to visualize which angles from [0,360] have the tangent equal to 1?

Answer 15

2tanC-3tanC= -tanC??

Answer 16

nvm got it

Answer 17

What you are doing is evaluating \(\tan ^{-1}1,\), or, in other woerds, you're finding the angle that has a tangent of 1.

Answer 18

tan1=45?

Answer 19

Which two angles in [0,360] have a tangent = to 1?

Of course, Lyubas, you don't have to accept or use my suggestion of replacing tan C with x temporarily.

The angle whose tangent is 1 is 45 degrees, yes, but there is another angle. Can you find it?

Answer 20

Please type this: tan1=45?

as either

arctan 1 = 45 degrees, or \[\tan ^{1-}1=45 \deg\]

Answer 21

I got tht so how do I find the 2nd angle?

Answer 22

or is this it?

Answer 23

Here's what to look for:

the tangent function is defined as \[\tan \theta=\frac{ opp }{ adj }\] where opp=opposite side and adj=adjacent side. OK with that?

Answer 24

yes

Answer 25

note that tan 45 deg = 1/1 (both the opp side and the adj side are 1).

Note that tan 225 deg = -1/(-1) (both the opp side and the adj side are equal to -1 in the third quadrant). So the 2nd solution is 225 deg.

You might want to draw this situation; doing so may make the situation clearer for you.

Answer 26

got it thnks answer : 45,225 ?

Answer 27

Yes! You could improve this answer by writing it as theta: {45, 225}.

Answer 28

If you're completely satisfied with this solution and the methods we used, move on to another problem. I'm sorry some of my responses have been slow; I have several others also waiting for help.

Answer 29

alrighty thx

Answer 30

Great working with you!

Answer 31

same here:)