Right Triangle Trigonometry

In a right triangle, the side opposite the angle being used is called the opposite side.  The hypotenuse is called the hypotenuse. The side touching the angle being used (but not the hypotenuse) is called the adjacent side.

Definitions:

sin A = opposite                                  csc A = hypotenuse
            hypotenuse                                            opposite

cos A = adjacent                                  sec A = hypotenuse
             hypotenuse                                           adjacent

tan A = opposite                                   cot A = adjacent
             adjacent                                                opposite
 

Special Angles

Angle 0o
= 0		 30o 
= p
   6		 45o
=  p
    4		 60o
=  p
    3		 90o
=  p
    2
Sin 0  \/0 = 0
  2		 \/1 = 1
  2    2		 \/2
  2		 \/3
  2		 \/4 = 1 
  2
Cos 0 \/4 = 1
  2		 \/3
  2		 \/2
  2		 \/1 = 1
  2    2		  \/0 = 0
  2

30o - 60o triangle

Draw a 30o - 60o triangle.  Draw another one congruent to it adjoining it.
We now have an equilateral triangle in which one side is 2r in length.
In the diagram, ML = 2r, MO = r, and LO must be found.  Let x be the length of LO.
 

Using the Pythagorean Theorem, r2 + x2 = (2r)2.
                                                  r2 + x2 = 4r2
                                                         x2 = 4r2 -  r2
                                                         x2 = 3r2
                                                           x = r \/3

Now, the values of the trigonometric functions for 30o and 60o can be found from the definitions.

45o - 45o triangle

Draw a 45o - 45o triangle.
Let r be the length of the two equal sides.
O is the right angle.
Let x be the length of the hypotenuse.

Using the Pythagorean Theorem, r2 + r2 = x2.
                                                        2r2 = x2
                                                         r \/2 = x

Now, the values of the trigonometric functions for 45o can be found from the definitions.

Problems

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