The Trigonometry Explorer
Great Explorations in Algebra, Geometry, and Science
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Resources
The Trigonometry Explorer provides a comprehensive overview of trigonometry fundamentals and helps students make connections from abstract concepts to the world around them. This engaging and easy-to-follow program builds many bridges from math to science, history, and everyday occurrences.
The Trigonometry Explorer offers something for every student of trigonometry. For those who need to review the basic building blocks of trigonometry, the creative, animated and engaging lessons on degrees, angles, and triangles provide a great starting place. The functions, piloting and inverse functions lessons are for those who have a grasp of the basics. For the student who is bored and uninspired with trigonometry, the applications on radio waves, sound, surveying, and many more show how trigonometry is used to explain everyday phenomena and solve real world problems.
Program Outline
- Degrees
- Definition of degrees, positive and negative degrees, right angle
- Latitude and Longitude
- Angles
- Create angles, angles in standard position, coterminal angles, reference angle, angle names
- Sextant
- Radians
- Pi defined and explored, arclength defined, radians, 2pi radians in a circle, converting degrees to radians, and radians to degrees.
- Eratosthenes
- Triangles
- Create triangles, triangle types, triangle properties, triangle area.
- Trusses - bridges
- Right Triangles
- Pythagorean Theorem, hypotenuse, adjacent, opposite, ratio of sides, indirect measurement.
- Pythagoras
- Functions
- Right triangle in a Cartesian coordinate system, trig functions, explore right triangles in X-Y System, explore trig relationships, trig function signs, reciprocals
- Parallax, Clinometer, Surveying (Law of Sine)
- Plotting
- Explore amplitude, period and phase shift of sine, cosine and tangent
- Introduces waves
- Sounds, Radio Waves, Color and Light, Addition of Ordinances
- Inverse Functions
- Arcsine, arccosine, arctangent, standard position angle using the arctangent
- Refraction, Polar Coordinates, Pythagorean Identity
Educational Benefits
- Problem Solving
- Proportional Reasoning
- Connections Outside Math
- Connections Withing Math
- Algebraic Reasoning
- Equation Solving