# Free Trigonometry Questions and Problems

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.

## Interactive Trigonometry Tutorials (Applets)

### Trigonometric Functions

• Periods Of Trigonometric Functions. The periods of all 6 trigonometric functions are explored interactively using an applet.
• 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 such as period, phase shift, asymptotes, domain and range.
• Graph of Sine, a*sin(bx+c), Function. Graphing and sketching sine functions of the form f (x) = a*sin (bx + c; step by step tutorial.
• 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).

### Unit Circle in Trigonometry

• 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.
• Unit Circle And The Trigonometric Functions sin(x), cos(x) and tan(x). Using the unit circle, you will be able to explore and gain deep understanding of some of the properties, such as domain, range, asymptotes (if any) of the trigonometric functions.

## 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.

## Problems and Self Tests

• 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.