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SPECIAL RIGHT TRIANGLES AND CIRCULAR TRIGONOMETRY

In a previous unit we learned that every acute angle measure in a right triangle is uniquely associated with the reduced ratio of the sides of that triangle. For all the possible measures for these acute angles greater than zero degrees and less than ninety degrees, three angle measures are deemed to be critical because of the special ratios that exist in the sides of triangles when these angles are present. This unit will examine these “critical values” in the two special right triangles where they are found. To further examine these special ratios, the right triangles will be inscribed at various positions inside a circle which is centered at the origin of the xy-plane. From this diagram, values for the six trigonometric ratios for these triangles will be deduced and later graphed using the graphing calculator. Once graphed, the standard curves of the six trigonometric ratios can be analyzed.

 Special Right Triangles (04:25)
 
 
 Polar Coordinates:  Radar Blips (05:12)
 
 The Unit Circle (07:07)
 




Below are additional educational resources and activities for this unit.
 
Trigonometric Ratios
 
Special Right Triangles