Sine Squared

Date: 06/27/2003 at 09:41:49
From: Tennis gal
Subject: Trigonometry

What is sine squared, and how do you enter it in a calculator?

Date: 06/27/2003 at 10:16:57
From: Doctor Ian
Subject: Re: Trigonometry

Hi, 

The notation

     2
  sin (x)

means exactly the same thing as

          2
  (sin(x))

but it's easier to write, because it uses fewer symbols. 

(Mathematicians are very big on finding ways to write as few symbols
as possible, which is why we write

  2.79

instead of 

  2 + 79/100

They mean the same thing, but the former requires only half as many
symbols as the latter.) 

So to compute something like 

     2
  sin (30 degrees)

you would compute the sine of 30 degrees, and then square the result. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 06/27/2003 at 10:20:06
From: Tennis gal
Subject: Trigonometry

I don't understand how you are supposed to use trig on a triangle that 
is not a right triangle...

Date: 06/27/2003 at 10:39:05
From: Doctor Ian
Subject: Re: Trigonometry

Hi, 

The sine or cosine of a particular angle doesn't depend on whether the
angle is part of a right triangle or not.  For example, consider the
parallelogram below:

       ___________
      /          /
     /          /
    /          /
   /  o       /
  /_60_______/

The cosine of this 60 degree angle is 1/2, even though there isn't a
right angle anywhere in sight.  But note that we can always _make_ a
right triangle by dropping an appropriate altitude, e.g., 

       ___________
      /          /
     /.         /
  c / . a      /
   /  .       /
  /___.______/
    b

Here, we know that the sine of the angle is sqrt(3)/2, so we know that

  a   sqrt(3)
  - = -------
  c      2

which means that if we know the length of side c, we can use that and
the angle to find the height of the parallelogram.  

We could do something similar starting from a scalene triangle:

       
      . 
     .|  .          
  c . |     .    
   .  |a       . 
  . . | . . . . . .
   b


So one way to answer your question is to say that you use trig on a
triangle that isn't a right triangle by using an altitude to turn it
into a pair of right triangles. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/