|
t-formula in
trigonometry |
|||
|
The t-formula can
change trigonometric functions into half-angles and may be described
as follows: Let then The
t-formula is very helpful in solving trigonometric equations by changing them
to algebraic equations in t. The t-formula can also be employed to find the
maximum and minimum of certain trigonometric functions. Certain integrals can
be evaluated by t-formula. This
small article shows some proofs of t-formula. |
|||
Method
1
|
|||
Method
2
Draw
a right angled triangle:
The
hypotenuse AC can be calculated using Pythagoras Theorem. Then reading from the triangle, we get: |
|||
Method
3
Draw
a right angled triangle, The hypotenuse AC can be found using Pythagoras
theorem: Reading
from the triangle, we can get: |
|||
Exercise
Can
you prove the t-formula using the following diagram:
|
, 
