Free tutorials and problems on solving trigonometric equations, trigonometric identities and formulas can also be found. Java applets are used to explore, interactively, important topics in trigonometry such as graphs of the 6 trigonometric functions, inverse trigonometric functions, unit circle, angle and sine law.
Properties of The Six Trigonometric Functions. The properties of the 6 trigonometric functions sin (x), cos (x), tan (x), cot (x), sec (x) and csc (x) are discussed. These include the graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points.
Sine Function. The sine function f(x) = a*sin(bx+c)+d is explored, interactively, using a large applet.
Cosine Function. An applet helps you explore the general cosine function f(x) = a*cos(bx + c) + d.
Tangent Function. The tangent function f(x) = a*tan(bx+c)+d
and its properties such as graph, period, phase shift and asymptotes by changing the parameters a, b, c and d are explored interactively using an applet.
Secant Function. The secant function f(x) = a*sec(bx+c)+d and its properties such as period, phase shift, asymptotes domain and range are explored using an interactive applet by changing the parameters a, b, c and d.
Cosecant Function. The cosecant function f(x) = a * csc ( b x + c) + d and its period, phase shift, asymptotes, domain and range are explored using an applet.
Cotangent Function. The cotangent function f(x) = a * cot ( b x + c) + d is explored along with its properties susch as period, phase shift, asymptotes, domain and range.
Graphs of Basic Trigonometric Functions. The graphs and properties such as domain, range, vertical asymptotes of the 6 basic trigonometric functions: sin(x), cos(x), tan(x), cot(x), sec(x) and csc(x) are explored using an applet.
Sum of Sine and Cosine Functions. An interactive tutorial to explore the sums involving sine and cosine functions such as f(x) = a*sin(bx)+ d*cos(bx).
Trigonometric Equations and the Unit Circle. The solutions of the trigonometric equation sin(x) = a, where a is a real number are explored using an applet. Both the graph of sin(x)and the unit circle are used to explore the solutions of this equation as a changes.
Trigonometry Angle Questions With Answers. Trigonometry questions related to angles in standard position, coterminal angles, complementary and supplementary angles, as well conversion from degrees to radians and vice versa, are presented. The solutions and answers are provided.
Analytical Trigonometry Tutorials (Problems, Examples with solutions)
Solving Trigonometric Equations
Trigonometric Equations. Tutorial with detailed explanations on how to solve trigonometric equations using different methods and strategies and the properties of trigonometric functions and identities.
Solve Problems Using Trigonometric Ratios. A set of problems with detailed solutions are presented. These problems have been designed to reinforce the use of the trigonometric ratios and Pythagora's theorem.
Tutorial on Sine Functions (2)- Problems. This is a tutorial on the relationship between the amplitude, the vertical shift and the maximum and minimum of the sine function.
Solve Trigonometric Equations. 10 problems, with their answers, on solving trigonometric equations are presented. These may be used as a self test on solving trigonometric equations.
Test on Graphs Trigonometric Functions. A set of questions, with their answers, on identifying the graphs of trigonometric functions sin(x), cos(x), tan(x), sec(x), csc(x), cot(x) are presented. These may be used as a self test on the graphs of trigonometric functions.
Trigonometric tables. Trigonometric tables of all 6 trigonometric functions, with angles in degrees and radians. Copies of these tables can be downloaded.