Special Angles

Hi everyone this is Nick. Today in class we learned about Special Angles and more questions that deal with them.                     

Note: In order to understand this you must be familiar with the reference triangles from before.

 An example of a question we did in class was this one where we had to prove this statement is true:

 Cos^2 pie/6= (sin Pie/3)(cos Pie/6)

The first step is to find values for all the different trig functions in the question

Cos Pie/6              and           Sin Pi/3

Once we recognize what we're looking we use the reference angles to figure out values:

Cos Pie/6

Pie/6 = 30 degrees 

   

so we use the reference triangle to get values for Cos

 

We know Cos = A/H therefore Cos Pie/6 = Root 3/2

Sin Pie/3

Pie/3 = 60 degrees

We know Sin = O/H therefore Sin Pie/3 = Root 3/2

Now we substitute in the values:

cos^2 Pie/6 =  (sin Pie/3)(cos Pie/6)

                      after input

(root 3/2)^2 = (Root 3/2)(Root 3/2)

Now we solve:

3/4 = (Root 3/2)^2  

3/4 = 3/4  therefore the equation is true. 

Hope this helps, Later!