Derivation through first principle sin 2x?

9514 1404 393

Explanation:

Consider the attached diagram.

Arc RB is centered at O and has a radius of 1. Angle ROD is designated angle α. It is duplicated as angle DOB, meaning that OD is the perpendicular bisector of chord RB. Triangles DFB and RGD are congruent (by HA). They are similar to triangle RDO by AA similarity.

Now, we can use the definitions of sine and cosine to find some segment lengths. Since the circle is of radius 1, the length RD is sin(α). Then, in triangle RGD, the length DG is sin(α)·cos(α). As we said, BF is congruent to DG, so the length BH is 2·sin(α)·cos(α). Again, by the definition of sine, BH = sin(2α). So, we have ...

  sin(2α) = 2·sin(α)·cos(α) . . . . the desired relationship

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw