EIT Exam Trignometry

1. Degree and Radians

Radians x 180/3.14 = Degree

Degree x 3.14/180 = Radians

2. Plane Angles

Acute Angle - Less than 90'
Obtuse Angle - More than 90'
Right Angle -90'
Straight Angle - 180'
Refles angle - More than 180'


5. Triangle





4. Right Triangle


5. General Triangle
Law of Cosines


6. Trigonometric Identities
Law of Cosines


7. Hyperbolic Functions and Identities
Law of Cosines

8. Fourier Series
Fourier Theorem

Fourier Series problem solving

Parseval Relation

6 (a) What is the mean value, over one period, of (f(t))^2 in 
   question 2(i)?
 
   (b) Using Parseval's theorem and the Fourier series for the 
   square wave of part (a), show that
 
            1     1     1     1          pi^2
           --- + --- + --- + --- +... =  ----
           1^2   3^2   5^2   7^2          8

(a) (f(t))^2 = 1 for -pi < t < 0 and = 0 otherwise.
    Its mean value is thus area/period = pi * 1/(2 pi) = 1/2.

(b) The Fourier coefficients for this function are

    a0 = 1, an = 0 for n >0; 
    bn = -(2/n pi) for n odd, 0 otherwise.

    Parseval's theorem then tells us that

    mean(f^2) = (a0/2)^2 + (1/2) sum(an^2 + bn^2) n = 1...infinity.

    Hence

    1/2 = 1/4 + (1/2) (4/pi^2) [ 1/1^2 + 1/3^2 + 1/5^2 ...]

    Rearranging proves the result.