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# trig question

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1. The question is, 3Tanx - Tan^3x = 1 - 3 tan^2x

Im kinda confused on this i tried factorising it, but keep getting the wrong answers.
2. (Original post by SunDun111)
The question is, 3Tanx - Tan^3x = 1 - 3 tan^2x

Im kinda confused on this i tried factorising it, but keep getting the wrong answers.
Could you post how you factorised it?
3. (Original post by rayquaza17)
Could you post how you factorised it?
I took a factor of Tan X out and put it as Tan x ( 3 - Tan^2x + Tan x ) = 1
Kept getting wrong answers from it.
4. Let . Now try factorising:
i.e.
5. (Original post by Math12345)
Let . Now try factorising:
i.e.
wouldnt I use the factor theoram?
6. (Original post by SunDun111)
wouldnt I use the factor theoram?
Yep you can use that.
7. (Original post by Math12345)
Yep you can use that.

Right did it thanks, I kinda am stuck on an M1 question if you can help me. Basically 'The unit vectors I and J are directed North and east. A boat has initial velocity 4i + 6j ms and an initial position of 80I + 20j, it experiences an acceleration of -0.02i - 0.01j ms for 4 minutes. After 4 minutes the boat stops accelerating and continues with constant velocity for a further minute before hitting the bank and stopping, find the position of the point where the boat hits the bank.

Its quite long I know, but I worked out the position vector of the boat at Time T seconds, but im kinda struggling on how to work out the position vector for both times its really confusing.
8. (Original post by SunDun111)
Right did it thanks, I kinda am stuck on an M1 question if you can help me. Basically 'The unit vectors I and J are directed North and east. A boat has initial velocity 4i + 6j ms and an initial position of 80I + 20j, it experiences an acceleration of -0.02i - 0.01j ms for 4 minutes. After 4 minutes the boat stops accelerating and continues with constant velocity for a further minute before hitting the bank and stopping, find the position of the point where the boat hits the bank.

Its quite long I know, but I worked out the position vector of the boat at Time T seconds, but im kinda struggling on how to work out the position vector for both times its really confusing.
I've forgotten mechanics.
9. (Original post by SunDun111)
Right did it thanks, I kinda am stuck on an M1 question if you can help me. Basically 'The unit vectors I and J are directed North and east. A boat has initial velocity 4i + 6j ms and an initial position of 80I + 20j, it experiences an acceleration of -0.02i - 0.01j ms for 4 minutes. After 4 minutes the boat stops accelerating and continues with constant velocity for a further minute before hitting the bank and stopping, find the position of the point where the boat hits the bank.

Its quite long I know, but I worked out the position vector of the boat at Time T seconds, but im kinda struggling on how to work out the position vector for both times its really confusing.
Outline:

You have acceleration - you integrate that to get velocity (remember the +c and using the point t=0, v = 4i +6j to find the +c)

You then have (initial position) + (velocity) - plug t = 4 * 60 = 240 seconds to get the position after 4 minutes.

Now set up the new position as (position after 4 minutes) + t(constant velocity) and then plug t = 1 *60 = 60 seconds

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