Trigonometry and Complex Numbers
Collection of Trigonometry and Complex Numbers worksheets.
Table of Contents
- Measuring angles
- DMS → Decimal Angle Converter
- Decimal → DMS converter - Decimale → Sessagesimale
- Oriented Angles and the Unit Circle
- Trig functions
- Trig Functions and Plane Transformations - Lesson+Exploration
- Triangles
- The Law of Sines - Lesson+Practice
- Complex numbers
- Complex numbers: rectangular and polar form - Lesson
DMS → Decimal Angle Converter
Enter the values of Degrees (º), Minutes (') and Seconds ('') and press [i]Enter[/i] to convert the given angle in decimal form and view the steps of the conversion.
Trig Functions and Plane Transformations - Lesson+Exploration
Explore the plane transformations applied to the sine and cosine functions.[br][br]How does the function graph modify if we apply some "classic" transformations (horizontal and vertical translations, dilations, composition with [math]abs[/math] function, etc) ? [br][br]Before viewing the resulting graph, try to determine the new position of some "convenient" points related to the transformed function (e.g. the intersections with the [i]x[/i] and [i]y[/i] axes), as well as the possible variations of the main characteristics of the function (amplitude, period...).[br][br]Move the sliders to explore dynamically the magnitudes of translations and dilations, and drag point [i]P[/i] along the graph of the parent function to view the graph of the transformed one.[br][br]Deselect the [i]Instructions [/i]checkbox to start exploring transformations.[br]A button displayed on bottom right of the app allows you to delete traces.
The Law of Sines - Lesson+Practice
The [i]law of sines[/i] (or sine rule) relates the lengths of the sides of a triangle with the sines of its angles.[br][br]The apple below allows you to discover this useful law ([i]Theorem[/i]), learn how it is obtained ([i]Proof[/i]) and interact with a dynamic triangle ([i]Explore![/i]) to become familiar with this concept.
Solving a triangle means finding missing sides and angles - Let's solve one.
About the triangle in the app above, we know that [math]a=24[/math], [math]\beta=60°[/math] and [math]\gamma=45°[/math]. [br]Solve the triangle.
To be or not to be....
Use the law of sines to show if a triangle with:[br][math]a=18[/math], [math]b=36[/math] and [math]\alpha=45°[/math] does exist or not.[br][br]Explain you reasoning below.
Complex numbers: rectangular and polar form - Lesson
Rectangular and polar form of a complex number + geometric representation.