• Congratulations to the Class of 2024 on your results!
    Let us know how you went here
    Got a question about your uni preferences? Ask us here

Trig identity help (1 Viewer)

Footyking

New Member
Joined
May 25, 2013
Messages
9
Gender
Male
HSC
2013
hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 11
 

Footyking

New Member
Joined
May 25, 2013
Messages
9
Gender
Male
HSC
2013
hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 1
 

braintic

Well-Known Member
Joined
Jan 20, 2011
Messages
2,137
Gender
Undisclosed
HSC
N/A
hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 1
This is an Extension question, not 2 unit.

Do you do Extension, and have you learned the t-results or Auxiliary Angle method?

If not, you can still do it:
Let u=sin2x, so cos2x=sqrt(1-u^2)

The equation becomes 9 Sqrt(1-u^2) = 1-7u

Then square both sides, solve for u, then for x.

And finally as your solution involves squaring, check your answers by substitution, as squaring tends to introduce extra solutions.
 

braintic

Well-Known Member
Joined
Jan 20, 2011
Messages
2,137
Gender
Undisclosed
HSC
N/A
hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 11
Oops, check my response to your question in the 2 unit forum.
 

Footyking

New Member
Joined
May 25, 2013
Messages
9
Gender
Male
HSC
2013
Yes i do extension and i have learnt the t results, not the auxiliary angle method. Ive tried using t results and it didnt work for me, thats why i need help.
 

Footyking

New Member
Joined
May 25, 2013
Messages
9
Gender
Male
HSC
2013
sorry, i didnt understand the way you did it on the other post. can you do it by the t results? Do you expand the double angle before you use the t results or not?
 

Footyking

New Member
Joined
May 25, 2013
Messages
9
Gender
Male
HSC
2013
As stated from braintic's post: "Let u=sin2x, so cos2x=sqrt(1-u^2)"

u = sin 2x

Square both sides,

u^2 = sin^2 (2x)
u^2 = 1 - cos^2 (2x)
cos^2 (2x) = 1 - u^2
cos(2x) = sqrt{1-u^2)
Ok im really sorry but i did not learn how to do it that way, is there a chance you can show me by doing the t results?
 

braintic

Well-Known Member
Joined
Jan 20, 2011
Messages
2,137
Gender
Undisclosed
HSC
N/A
hi guys, ive been struggling with this question fora quite a while, i need help really badly.

The question is:

Find the possible values of tan x if: 9cos2x + 7sin2x = 11
Let t=tanx (tan of half the angle)

9(1-t^2)/(1+t^2) + 14t(1+t^2) = 11
9(1-t^2) + 14t = 11(1+t^2)
9 - 9t^2 + 14t = 11 + 11t^2
20t^2 - 14t + 2 = 0
You can solve that for t, replace t by tan x, then solve
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top