Question

help :( Solve the equation 2 tan C - 3 = 3 tan C - 4 algebraically for all values of C in the interval 0 degrees less than or equal to C < 360degrees.

Answer 1

@Hero

Answer 2

@Preetha

Answer 3

Try to isolate tan C.

Answer 4

uh, add 3 to the other side?

Answer 5

Yeah you can do that.

Just treat \(\tan C\) like \(x\)

Answer 6

\[2\tan C = 3\tan C - 1\] Now what?

Answer 7

Maybe subtract both sides by \(3\tan C?\)

Answer 8

so, 2tanC - 3tanC = -1
?

Answer 9

Yeah. Now combine like terms.

Answer 10

-1tanC = -1
?

Answer 11

Yep. What's the next step?

Answer 12

How to get rid of negative sign?

Answer 13

divide by -1
tanC = 1
sooo
tan^-1 (1) = 45

Answer 14

Yeah 45 degree is one of answers.

Maybe use unit circle?

Answer 15

I think i know how to do it now. Tangent is positive in quadrants 1 and 3, so i find the reference angle in those quadrants, right? and then check if they fit the interval?

Answer 16

yeah this is good way to do it.

Answer 17

thank you VERY much :)

Answer 18

No problem :0

Answer 19

:)*

Answer 20

I got {45 degrees, 225 degrees}.
:)