Hey fActor.
Can you show us what you have tried? (Also show us all the identities that you can derive from the information given). This approach is typically the best one when helping with these kinds of problems.
1. Show that OM = 6 cos θ - 2 sin θ
2. Show that area of triangle OAM is 10 sin 2(θ + α)
[OM = R cos (θ + α)]
[AM = R sin (θ + α)]
3. Given that θ can vary, find the maximum value of the area of triangle OAM.
Refer to: http://i49.tinypic.com/1pueqq.png
ABO & BNO = right angled triangles
OB = 6 cm
AB = 2 cm
line AM perpendicular to ON
Hello, fActor!
Code:A o *:* * : * 2 * :θ * * : * * : * B * P* - - o * 6 : * * * α * : * * * θ : * O o * * * * o * * o N M
Note that:
Let
Draw
1. Show that:
We see that: .
In
In
Therefore: .
2. Show that area of triangle is:
The area of
We note that: .
In
Therefore:
. .
. . . . . . . .
3. Given that can vary, find the maximum value of the area of
We have: .
Set the derivative equal to zero and solve.
. .
. .
Therefore:
. .