Super magic Hexagon for Trigonometric identities Tricks

~ Durai, Kugan

The super hexagon is a special diagram that helps the children to remember all the trigonometric identities and trigonometric functions visually [also requires memory].

How to draw the super hexogen

Draw the hexagon and we need to join all the opposite vertices and place the value 1 in the center of the hexagon.

Write the tan on the left vertex of the hexagon and use the quotient to identify the tangent ongoing clockwise, starting with tan = sin/cos.

Then add:

• cot (which is cotangent) on the opposite
  side of the hexagon to tan
• csc (which is cosecant) next, and
• sec (which is secant) last

Fill the reciprocal identities on the opposite side. Now the super magic hexagon is ready

Create Quotient identities

To understand the first set of formulae will let try around the hexagon in the clockwise direction, for the next set of directions will let try around the hexagon in the anti-clockwise direction.

Now we take any three continuing functions in the hexagon like  . If the product of the first and the third functions result in the function between them

Now focus on the function diagonally opposite vertices. They are reciprocal of each other

Focus the hexagon we found the six triangles. Focus only three triangle which s shadow in the image. Here we go clockwise within each one of the triangles starting with top left position. Square of the sum top two point of the triangle is equal to square off the bottom point of the triangle.

Anti-clock wise Here we go anti-clockwise within each one of the triangles starting with top left position. Square of the subtraction top two point of the triangle is equal to square off the bottom point of the triangle