Trigonometry

Trigonometry is kind of playing games with triangle and it attributes (angles θ & all 3 sides). here I’ve taken 2 triangles ∆ABC and ∆DEF with angle at A and F. If we are clear about sinθ and cosθ, then we can get all the other trigonometric formulas like tanθ as shown below,

Logical thinking is very important to Create formulas, derivatives or anything which you wish or like to build.

figure 1 :- Basic Trigonometry formulas

PS : Pythagoras Theorem is applicable only to Right Angled Triangle (i.e) at least any one of angle of triangle should be 90o

We have divided the Quadrants into 4 parts and get the values of sin, cos and tan for angles (0o, 30o, 45o, 60o and 90o) using this table values we can get values for any other angles as shown in the below figure.

figure 2 :- Angles and its values
figure 2.1 :- Angles and its values – continuation

By using the circle with a radius 1 units located at origin (0,0) and basic sin and cos formulas and derived the Trigonometry Identities.

figure 3 :- Identities

Like wise using basic trigonometric & Euler’s formula derived all forms of Identities

figure 4 :- Euler’s formulas