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# C2 Trig Help! Watch

1. Solve for t (theta), giving all roots in the interval 0 =< t =< 360:

1) 4sin^2 t cos t = tan^2 t.

Right so I started by doing the following:

4 - 4cos^2 cos t = sin^2 t / cos^2 t,
cos^2 t (4 - 4cos^2 cos t) = 1 - cos^2 t,
cos^2 t (4 - 4cos^3 t) = 1 - cos^2 t,
4 cos^2 t - 4 cos^5 t = 1 - cos^2 t,
Then use x = cos t to do:
4x^2 - 4x^5 = 1 - x^2,
= 5x^2 - 4x^5 - 1 = 0.

Is this right? If so, how would I factorise?
If it is incorrect, what is the correct way to do this?

Many thanks
2. Not sure if this is the best way either, but I found a more manageable solution.

Try dividing by the Sin^2(t) in the first equation and see where it takes you.
Not sure if this is the best way either, but I found a more manageable solution.

Try dividing by the Sin^2(t) in the first equation and see where it takes you.
Surely that would make it more difficult? And can you divide by sin^2 t in this case? Our teacher says it eliminates a solution or something...
Surely that would make it more difficult? And can you divide by sin^2 t in this case? Our teacher says it eliminates a solution or something...
Ah damn yeah, never thought about that. I have a habit of dividing by 0. 2 min.
5. x = 1 is a solution to the equation.
6. (Original post by jaheen22)
x = 1 is a solution to the equation.
How did you work it out?
How did you work it out?
Just by looking at it:

5(1)^2 - 4(1)^5 - 1 = 0
8. Anybody know if my method is correct and if so, how to factorise it to find the solutions?
9. 4sin^2(t)cos(t) = tan^2(t)
4sin^2(t)cos(t) = sin^2(t) / cos^2(t)
4sin^2(t)cos^3(t) = sin^2(t)
sin^2(t)[4cos^3(t) - 1] = 0

t = sin^-1(0) OR t = cos^-1((1/4)^(1/3))
t = ...
How did you work it out?
The equation is wrong though I think it should be:

4x^5 - 4x^3 - x^2 + 1 = 0

Where x = 1 is still a solution.
11. (Original post by Murrayland)
4sin^2(t)cos(t) = tan^2(t)
4sin^2(t)cos(t) = sin^2(t) / cos^2(t)
4sin^2(t)cos^3(t) = sin^2(t)
sin^2(t)[4cos^3(t) - 1] = 0

t = sin^-1(0) OR t = cos^-1((1/4)^(1/3))
t = ...
Cheers aha, this was bugging me. Seems I can't do C2 any more :P
12. (Original post by Murrayland)
4sin^2(t)cos(t) = tan^2(t)
4sin^2(t)cos(t) = sin^2(t) / cos^2(t)
4sin^2(t)cos^3(t) = sin^2(t)
sin^2(t)[4cos^3(t) - 1] = 0

t = sin^-1(0) OR t = cos^-1((1/4)^(1/3))
t = ...
Thanks a lot mate! Repped

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