Ayşe Naz's page

First Post:
 In our class we were solving questions about trigonometry (tangent and sine and cosine) and then out teacher gave us a sheet. In that sheet 

 there was a problem and problem was like this: There is a fire on the Woods building (Where preps have their lessons) and we are trying to save them. You must place the foot of the ladder 4 meters from the building or you might get hurt. We had a meter and a protractor gun. We used the meter to measure 4 meters and we placed the protractor gun there. With the help of the protactor gun we measured the angle between the floor and the top of the building. The angle was 45 which gave us a sense of proportion. Then we went all the way back to the doorway and measured the angle. The angle was 28. 













Then we constructed a triangle.

We inserted the angles we measured into the triangle and we solved it by saying that tangent 28 is equal to Height over 4 plus x. And tangent 45 is equal to Height over x. The rest is algebra but the important part in this question is to construct a triangle because it may be hard to solve these kinds of questions without a triangle.  The rest is algebra and you can find the answers here. ê

 Second Post:

Our teacher created a scavenger hunt for us and our task was to determine if ΔABC can be constructed when two lengths a and b and the measure of an acute angle A are given.There were papers around the classroom with specific conditions on them. You can see it in the first picture. For example in the condition A is like this: a is smaller than bsinA which would suggest that hypotenuse is smaller than the other side. So we cannot construct a triangle like this so the answer is 0. The triangle is posted below and decide for yourself if or how many triangles can be constructed with condition B, C and D. In the last photo you can see me and my group working on this 

task.

Third Post:

"This month, our unit was trigonometric functions and identities.  We did double angle values (cos(2x)) and finding the value of the sum of two angles (sin(x+y)). We solved many questions and here are some examples. The questions are from Turkey’s university entrance exam in 2013 and 2012. The following equations are needed to solve these questions:

 

Sin(2x)= 2sin(x)cos(x)

Tip: You can find sin(4x) by putting 2x instead of x into the equation 25 lys 12. 

Tan(x+y)= (tanx+tany)/1-(tanx.tany)

Tip:You might want to use this one in question 24(lys 12).  It is always easier to use this formula when a square is given and a diagonal is formed and the question is asking for a angle formed between the diagonal and a line.

A tip for Lys 12 question 26: If a perfect square is given and has sin^2(x) and cos^2(x), the first step should be to put the value into the x. The next step should be changing cos^2(x) into sin^2(x) (just saying cos and sin here might make it easier to understand) which is 1-sin^2(x). And the rest is algebra.

I solved the questions and the answer key/solutions are attached."

Fourth Post:

Our current topic: Sequences and Series

First let’s get to know the tower of Hanoi:

The tower of Hanoi, is a puzzle invented by E. Lucas in 1883. In this game you must move all the disks from Tower 1 to Tower 3 in least number of moves.  You are never allowed to put a bigger disk on top of a smaller disk and you may only move one disk at a time.

Here is how you find the minimum number of moves:

Let Mn represent the minimum number of moves needed to move n disks from Tower 1 to Tower 3.

Try this with first

M1=1

M2=3

M3= 7

M4= 15

M5=31

Can you see a pattern here?

Yes its first multiplying M(n-1) with two and adding one!

 The equation for the minimum number of moves: Mn= 2M(n-1) +1

Here is some proof: To transfer n disks from Tower 1 to Tower3, first transfer (n-1) disks from Tower 1 to Tower 2 (This takes M(n-1) moves) Then move the nth disk to Tower 3 (one move) Finally transfer (n-1) disks from Tower 2 to 3 (M(n-1) moves)
So Mn= 2M(n-1) +1


(Special thanks to Ms. Şenocak) 

Now Play and See if you can move it in  least number of moves!

http://www.dynamicdrive.com/dynamicindex12/towerhanoi.htm