1.  Using your page's general settings, press the “Show Axis” and “Show Grid” buttons.[br]For the grid, select the major grid lines section.[br]2.   From the “Circle: Center & Radius” section, create a circle with the center point (0, 0) and a radius of 1 cm. Name the center point “O”.[br]3.   Using the “Slider” tool, create a slider and select the angle type, then from the settings of it, name the slider as “angle and from the section “Slider” set min and max points to 180° and 360° respectively. [br]4.  Create a point on the circle and in the first quadrant of the coordinate plane, and name it as P. In the “Definition” section of this point, write “(cos(angle), sin(angle))”. This will ensure that your point P can only move on the circle within the first and second quadrants of the coordinate plane.[br]5.  Similarly, place a point at (1, 0), and name it as A.[br]6.  Use the “Segment” tool to create a new PO segment. [br]7.  Measure the AOP angle (α) with the “Angle” tool. Change the angle of the slider and make sure your AOP angle only moves between 0° and 180°.[br]8.  Using the “Perpendicular Line” tool, create a line passing through point P and the x-axis.[br]9.  Place a point where the line you created intersects the x-axis, and named it as B. Again, using the segment tool, create a new PB segment.[br]10.  Hide the line you created in the 8[sup]th[/sup] step from the settings by deselecting the show object.[br]11.  Using the segment tool again, create the BO segment. You now have a right triangle[br]that can only move in the first and second quadrants of the coordinate plane.[br]12.  Let's change the style of this right triangle a little. To make its edges more distinct, go to the “Color” tab in the settings section and make them black. Change the name of the PO segment to “1” in the “Caption” section. Similarly, let's call the PB segment “a” and the OB segment “b”.[br]13.  Now we will change the appearance of the AOP angle. To do this, first open the “Style” tab in the settings section and change the appearance of the angle to a clockwise rotating arrow shape in the “Decoration” section.[br]14.  Again, go to the settings section of the same angle and write “α< 90°” in the “Condition to Show Object” field in the “Advanced” section. [br]15.  Create a new point on the circle with coordinates (0, 1), and name it as C.[br]16.  Use the “Angle” tool to create the COP angle, and name it as β.[br]17.  Use the “Text” tool to create a text, and name it as text1, and go to the geometry section in the “Advanced” tab, open a new (empty box) and enter “[b]If(α [/b][b]≟ 90[/b][b]°, [/b][b]” 90[/b][b]° [/b][b]“, 1[/b][b]° < [/b][b]α < 90[/b][b]°, [/b][b]”90[/b][b]° - [/b][b]“ [/b][b]β, [/b][b]α [/b][b]≟ 0[/b][b]°, [/b][b]” 0[/b][b]°“, [/b][b]α [/b][b]≟ 180[/b][b]°, [/b][b]” 180[/b][b]°“, 90[/b][b]° < [/b][b]α < 180[/b][b]°, [/b][b]”90[/b][b]° + [/b][b]“ [/b][b]β)[/b]”. [br]18.  Go to the settings section of the AOP angle, select text1 from the “Use Text as Caption” section. [br]19.  Go to the settings of text1 and make it invisible by deselecting “Show Object”. With this step, your main triangle is complete. [br]20.  Now change the color of the AOP angle and your slider to blue using the “Color” segment in the settings section. [br]21.  You may have noticed that when you set the “angle” slider to greater than 90°, your AOP angle disappears. Now we will create a new angle that will be an arrow pointing counterclockwise when it is greater than 90°. To do this, use the “Angle” tool to select a new AOP angle, but its name should be a different symbol, such as “γ”.[br]22.  Go to the settings section of the new angle (γ) and write “γ> 90°” in the “Condition to Show” section of the “Advanced” tab.[br]23.  In the “Style” tab of the same angle's settings section, change the appearance of the angle to an arrow pointing counterclockwise and select blue as the color in the “Color” tab.[br]24.  Then, use the “Text” tool to create “text2” and, as with text1, open a dynamic box in the advanced section and write “[b]If(180° > γ > 90°, ”90° + “ β, γ [/b][b]≟ 180[/b][b]°, [/b][b]”180[/b][b]°“)[/b]” inside it.[br]25.  Go to the settings section of the “γ” angle, check the “Use Text as Caption” box, and select “text2”. Then hide text2 from the settings section.[br]26.  Now we will create another similar right triangle. This time, create another perpendicular line from point P to the y-axis using the “Perpendicular Line” tool.[br]27.  Place a point where the line intersects the y-axis, and name it as D. Use the segment tool to create a new PD segment.[br]28.  Create a new segment as OD and make the line invisible in the settings section.[br]29.  Change the style of the PD and OD sides of this new right triangle you created to dashed lines using the “Line Style” section in the “Style” tab in the settings section. You can also make their colors red in the “Color” tab. [br]30.  Let's label the PD edge and OD edge as “a” and “b” respectively in the “Caption” section of the settings. [br]31.  Change the COP angle in the “Style” section of the settings by increasing its size and set its color to gray in the “Color” segment. This will make it easier to distinguish from the AOP perspective.[br]32.  Next, we need to add the dynamic texts we want to appear on the sides of the page when we change the slider. To do this, create a new text, name it as text3. [br]33.  Write the following inside text3: “cos([b]text1[/b])=sin([b]β[/b])=b [b]If(β [/b][b]≟ 0[/b][b]°, [/b][b]”=0[/b][b]“, [/b][b]β [/b][b]≟ 90[/b][b]°, [/b][b]”=1[/b][b]“)[/b]”. The text highlighted in [b]bold[/b] is dynamic text, meaning it will appear inside the dynamic boxes we opened in the “Advanced” section. The remaining parts are static, meaning they will be written as they are.[br]34.  Select text3 again and select the “Serif” and “La TeX formula” boxes.[br]35.  Create a new text as text4. Write “sin([b]text1[/b])=cos(β)=a [b]If(β[/b] [b]≟ 0[/b][b]°, "=1", β[/b] [b]≟ 90[/b][b]°, "=0")[/b]” inside it. In this text, the [b]bold[/b] text is also dynamic text, while the rest is static text. [br]36.  Similarly, select “Serif” and “La TeX formula” for text4.[br]37.  Create a new text as text5. Inside it, write “tan([b]text1[/b])=cot(β)= \frac{a}{b} [b]If(β [/b][b]≟ 0[/b][b]°, "=\frac{1}{0}=undefined", β [/b][b]≟ 90[/b][b]°, "=\frac{0}{1}=0")[/b]” and select the “Serif” and “La TeX formula” boxes.[br]38.  Create another new text as text6. Inside it, write “cot([b]text1[/b])=tan(β)= \frac{b}{a} [b]If(β[/b][b] ≟ 0[/b][b]°, "=\frac{0}{1}=0", β[/b][b] ≟ 90[/b][b]°, "=\frac{1}{0}=undefined")[/b]”  and select the “Serif” and “La TeX formula” boxes.[br]39.  Now open the settings for text3, text4, text5, and text6 and write “90° ≥ α ≥ 0°” in the “Condition to Show Object” field in the “Advanced” tab.[br]40.  These texts we created are for the first quadrant of our triangle on the coordinate plane. Therefore, we should place these texts one below the other on the side of the coordinate plane corresponding to region 1.[br]41.  Now, in a similar way, we will write 4 more texts, and these will be for region 2, and we will also arrange them on the side of region 2. This way, the similarities and differences between the two regions will be easier to see.[br]42.  We will create a new text, named “text7”, and its content will be similar to text3, as follows: “cos([b]text1[/b])= -sin(β)= -b [b]If(β[/b] [b]≟ 0[/b][b]°, "=0", β[/b] [b]≟ 90[/b][b]°, "= -1")[/b]”.[br]43.  We will create a new text, named “text8”, and its content will be similar to text4, as follows: “sin([b]text1[/b])= -cos(β)= -a [b]If(β[/b] [b]≟ 0[/b][b]°, "= 1", β[/b] [b]≟ 90[/b][b]°, "=0")[/b]”.[br]44.  We will create a new text, named “text9”, and its content will be similar to text5, as follows: “tan([b]text1[/b])=cot(β)= - \frac{a}{b} [b]If(β [/b][b]≟ 0[/b][b]°, "=\frac{1}{0}=undefined", β [/b][b]≟ 90[/b][b]°, "=\frac{0}{1}=0")[/b]”.[br]45.  We will create a new text, named “text10”, and its content will be similar to text6 as follows: “cot([b]text1[/b])=tan(β)= -\frac{b}{a} [b]If(β[/b][b] ≟ 0[/b][b]°, "=\frac{0}{1}=0", β[/b][b] ≟ 90[/b][b]°, "=\frac{1}{0}=undefined")[/b]”.[br]46.  text7, text8, text9, and text10 will all be in “Serif” and “La TeX formula” format, and the “Condition to Show Object” field will contain “180° ≥ α > 90°”.  [br]47.  After placing the texts in a regular order on the screen, your activity is ready, change the “angle” and see what is happening![br][br][br]