RELATIONS BETWEEN THE TRIGONOMETRICAL RATIOS OF SOME ANGLES
Section: Geometry
 

1. COMPLEMENTARY ANGLES

Complementary angles add up to 90º. In the following window you can see angle B (in red) and its complementary angle, angle A (in green)

1.- Change the size of angle A and watch how its complementary angle also changes size.

2.- What does the sine of angle A always coincide with? What about its cosine?

3.- Find a connection between the tangents of angle A and angle B.


2. SUPPLEMENTARY ANGLES

Supplementary angles add up to 180º. In the following window you can see angle B (in red) and its supplementary angle, angle A (in green).

1.- Change the size of angle A and watch how its supplementary angle also changes size.

2.- What do the sine values of supplementary angles have in common? What about their cosine values?

3.- What's the relation between the tangents of supplementary angles?

4.- If an angle is found in the fourth quadrant which quadrant does its supplementary angle belong to? What about its complementary angle?

Use the Init button to restore the initial values.


3. ANGLES WITH A DIFFERENCE OF p radians.

In the following window you can see that there is a difference of p radians between angles A and B.

1.- Change the size of angle A and watch how angle B also changes size.

2.- What do the sine values of angles A and B have in common? What about their cosine values?

3.- What's the relation between the tangents of angles A and B?

Use the red and blue A control keys to change the size of angle A, or write the new value directly into the box and press the Enter key.


4. OPPOSITE ANGLES  

In the following window you can see angle B (in red) and its opposite angle, angle A (in green).

1.- Change the size of angle A and watch how its opposite angle also changes size.
Prove that
B = 2p - A.

2.- What do the sine values of the opposite angles have in common? What about their cosine values?

3.- What's the relation between the tangents of two opposite angles?

 


       
           
  Pedro Férez Martínez
 
Spanish Ministry of Education. Year 2001
 
 

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