TRIGONOMETRIC FUNCTIONS 

DEFINITION OF TRIGONOMETRIC FUNCTIONS FOR A RIGHT TRIANGLE 

Triangle ABC has a right angle (90°) at C and sides of length a, b, c. The trigonometric functions of angle A are denned as follows  
sine of A = sine A = 

RELATIONSHIP BETWEEN DEGREES AND RADIANS 

A radian is that angle e subtended at center O of a circle by an arc MN equal to the radius r. Since 2a radians = 360° we have 1 radian = 180°/π = 57.29577 95130 8232. . .° 1° = π/180 radians = 0.01745 32925 19943 29576 92. . .radians 

RELATIONSHIPS AMONG TRIGONOMETRIC FUNCTIONS 

SIGNS AND VARIATIONS OF TRIGONOMETRIC FUNCTIONS 

EXACT VALUES FOR TRIGONOMETRIC FUNCTIONS OF VARIOUS ANGLES 

GRAPHS OF TRIGONOMETRIC FUNCTIONS 

FUNCTIONS OF NEGATIVE ANGLES 



ADDITION FORMULAS 

FUNCTIONS OF ANGLES IN ALL QUADRANTS IN TERMS OF THOSE IN QUADRANT I 

RELATIONSHIPS AMONG FUNCTIONS OF ANGLES IN QUADRANT I 

DOUBLE ANGLE FORMULAS 

HALF ANGLE FORMULAS 

MULTIPLE ANGLE FORMULAS 

POWERS OF TRIGONOMETRIC FUNCTIONS 



SUM, DIFFERENCE AND PRODUCT OF TRIGONOMETRIC FUNCTIONS 



GENERAL FORMULAS 

INVERSE TRIGONOMETRIC FUNCTIONS 

If x = sin y then y = sin¹x, i.e. the angle whose sine is x or inverse sine of x, is a manyvalued function of x which is a collection of singlevalued functions called branches. Similarly the other inverse trigonometric functions are multiplevalued. For many purposes a particular branch is required. This is called the principal branch and the values for this branch are called principal values. 

PRINCIPAL VALUES FOR INVERSE TRIGONOMETRIC FUNCTIONS 



Relations Between Inverse Trigonometric Functions 



Graphs Of Inverse Trogometric Functions 

RELATIONSHIPS BETWEEN SIDES AND ANGLES OF A PLANE TRIANGLE 

The following results hold for any plane triangle ABC with sides a, b, c and angles A, B, C. 

Law of Sines Law of Cosines 

RELATIONSHIPS BETWEEN SIDES AND ANGLES OF A SPHERICAL TRIANGLE  
Spherical triangle ABC is on the surface of a sphere as shown in Fig. above Sides a, b, c [which are arcs of great circles] are measured by their angles subtended at center O of the sphere. A,B,C are the angles opposite sides a, b, c respectively. Then the following results hold. 

Law of Sines Law of Cosines Law of Tangents


NAPIER'S RULES FOR RIGHT ANGLED SPHERICAL TRIANGLES 

Except for right angle C, there are five parts of spherical triangle ABC which if arranged in the order as given in Fig. would be a, b, A, c, B. 

Suppose these quantities are arranged in a circle as in Fig above where we attach the prefix co [indicating complement] to hypotenuse c and angles A and B.
Since coA=90°A, coB = 90°B, sin (coA) = cos a cos (coB) or cos A = cos a sin B 