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## 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.
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Shared by masvgp

Material Type
Worksheet
Tags
trigonometry
Target group (age)
19+
Language
English (UK)

GeoGebra version
4.0
Views
795
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