Question

Rewrite the expression as a trigonometric function of a single angle measure.

Answer 1

\[\frac{ \tan4 \theta + \tan 2 \theta }{ 1 - \tan 4 \theta + \tan 2 \theta }\]

Answer 2

hi. do you still need help with this one?

Answer 3

Yes, I'm so lost on how to solve it

Answer 4

do you know the tangent addition formula?

Answer 5

tan(a+b)=(tan a +tan b)/(1-tan a tanb)

Answer 6

have you seen this formula before?

Answer 7

now think about the angle a=4theta and the angle b=2theta. does this help?

Answer 8

Ive seen it but never used it,

Answer 9

ah. well, your teacher is giving you the opportunity here

Answer 10

I'm confused on how I solve it with the this formula using the 'theta'

Answer 11

ok. well, it is more recognition than solving. look at the form of the equation i gave you and the relation you wrote above. write this puppy as the tangent of the sum of the two angles you have been given (4theta and 2theta)

Answer 12

it is good to ask questions if you are in doubt. :)

Answer 13

Sorry, If it takes to long to respond, I'm still confused a little so I'm trying to write it down so that would hopefully help me get it

Answer 14

no problem. so the form of the equation is tan (a+b)=(tan a +tan b)/(1-tan a tan b). substitute for a 4theta and for b 2theta

Answer 15

So, tan 4theta + tan 2theta / 1- tan 4theta * tan 2.?

Answer 16

we are interested in the left side. the tan (a+b) part. this condenses the mess you were given.

Answer 17

So 4 theta + 2 theta.?

Answer 18

which becomes tan ?

Answer 19

You would add the 4 & 2 together & get 6 & 6 would be the tan wouldn't it.?

Answer 20

perfect. yes!! so you tan 6theta, which is the trig function (tan) of a single angle 6theta.

Answer 21

Alright thank you for help.! :-) I understand this now.!