Trigonometric Ratios and the Unit Circle

Trigonometric Ratios and the Unit Circle Construction Instructions Type $x^{2} + y^{2} = 1$ into the input bar and press enter. Using the ``new point'' tool, put a point on the newly constructed circle. Using the ``perpendicular line'' tool, create a line perpendicular to the x-axis through the point on the circle. Using the ``segment between two points'' tool, create a line segment from the origin to the intersection of your perpendicular line and the x-axis. Using the ``segment between two points'' tool, create a line segment between the origin and the point on the circle. Using the ``segment between two points'' tool, create a line segment between the point on the circle and the intersection of the perpendicular line and the x-axis. Right click the perpendicular line outside the circle and click ``show object.'' Right click, in turn, each of the sides of the inscribed right triangle. Choose ``object properties.'' In the ``basic'' tab find the ``caption'' box, and type in an appropriate label choosing from hypotenuse, opposite, and adjacent. Then check the ``show label'' box, and select ``caption'' in the drop box to the right. In the ``object properties'' box choose the ``color'' tab and change the colors as desired. In the input tab type (sqrt(3)/2,1/2) and press enter. Then type (sqrt(2)/2, sqrt(2)/2) and press enter. Then type (1/2, sqrt(3)/2) and press enter. Hide all labels on all points by right clicking each one and choosing ``show label.'' Using the ``angle'' tool, click the point on the circle, then the point at the origin, then the point on the x-axis to construct the angle at the origin. Make sure the angle construction is for the first quadrant. Using the ``insert text'' tool, click on any white space convenient for making a label. Check the Latex box. Two dollar signs should appear in the edit box. In between the two dollar signs type the following: \Big( \frac{sqrt3}{2}, \frac{1}{2} \Big). Then click ``OK'' and move the label to the appropriate point. Repeat this process for each of the remaining points changing the numbers in the \frac{}{} command to the correct numbers. I recommend copying the formula and pasting it each time, so as not to have to type in again.

 

masvgp

 
Resource Type
Activity
Tags
circle  ratios  trigonometry  unit-circle 
Target Group (Age)
19+
Language
English (United Kingdom)
 
 
GeoGebra version
4.0
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