Trigonometric Functions and Identities Index

Right angled triangle and Application of right angled triangle

Right angled triangle and Application of right angled triangle

Right Angled Triangle:   In a right angled triangle, ABC with sides BC = a CA = b and AB = c ;     We know that: or , And or , And or ,   It is obvious that SIN A = COS B , COS A = SIN B because: A+B = 90 , So A is the complement angle of B , this may be stated as: Sine of the angle A = Sine of the complement of B So , Sine of the angle A = CoSine of angle B Or , And similarly: and     In a triangle , there are three angles and three sides. They are known as the six components or elements of a...

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Trigonometric functions of negative angles

Trigonometric functions of negative angles

Trigonometric functions of negative angles:   let and be any two angles equal in magnitude but opposite in sign. If we place each of them in the standard position it can be observed that the two angles are symmetrically placed on either side of x-axis. Suppose we construct a circle of radius “r” with centre “o” , it will cut the terminal arms of angles and as shown in figure below:   Let thee points “P” and “P’” respectively. Clearly , the abscissa of P is the same as that of...

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Pythagorian Identities

Pythagorian Identities

  Let “OPQ” be a triangle where angle POQ is , and it’s base be “x” and perpendicular “y” as shown in the picture below:   Then, Appealing to the Pythagorian theorem, we have: Now let us suppose op be “r” then: And as: and   We have: Thus: This is called the fundamental Pythagorian identity of trigonometry. From this we can also develop other identities as:   Dividing both side of fundamental Pythagorian identity by   Hence ,   And now dividing both...

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Properties of trigonometric functions

Properties of trigonometric functions

Properties of trigonometric functions: It is often useful to remember and use the properties of trigonometric functions while applying trigonometry in real life. The main properties among the properties of trigonometric functions are given below:   a> Quadrant rule of signs: In first quadrant both abscissa and ordinate are positive or ,   , so sine , cosine , tangent and all other trigonometric functions in this quadrant are positive. But in second quadrant thus in second quadrant: and we can also analyze third and fourth quadrant...

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Trigonometric Functions

Trigonometric Functions

Trigonometric Functions: We have already defined the trigonometric functions such as sine , cosine , tangent of any magnitude already here: trigonometric functions Now , we consider trigonometric functions for angles of a right angled triangle , and see how they are a special case of trigonometric functions of angle of any magnitude.   Suppose ABC is a right angled triangle with hypotenuse “c” ,  “a” the side opposite to the angle and “b” the side adjacent to the angle , as shown in the figures...

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