Trigonometry Final Exam Learning

Introduction 

                     Trigonometry is the devision of mathematics which represents with the triangles particularly the right triangles, circles and waves. Trigonometry also considers oftan time colecting helps in estimation / figuring such as logarithms. Trigonometry is also used in the field of engineering. In early days trigonometric tables were used in astronomy, it is used to find the height and distance between the objects which are too far. For example, distance between stars and earth can be determined using trigonometry.

Let us some functions of trigonometry and sample problems for learning final exam.

 

Functions of trigonometry for learning final exam:

 

These are the functions used in trigonometry problems  and explanations of each below.

Angles:
    It is the measure of rotation between two lines.

Quadrant:
    The x-y plane which is divided into four regions called quadrants.

Sine function:
    It is an odd function ranges between -1 and 1. The time period for the completion of one cycle is 2`pi` . It is symmetric with origin (0,0).

Cosine function:
    It is an even function that ranges between -1 and 1. The time period for one cycle is 2`pi` and is symmetric with y-axis.

Tangent function:
    It is an odd function. The time period for one cycle is `pi`. Tangent function is symmetric with respect to the origin.

Secant function:
    It is an even function and is symmetric with y-axis. Secant function ranges between [-∞, -1] and [1, +∞]. Its time period is 2`pi`.

 

Cosecant function:
    It is an odd function that ranges between [-∞, -1] and [1, +∞]. It is symmetric with origin and time period is 2`pi`.

Cotangent function:
    It is an odd function, symmetric with origin. The time period for one cycle is `pi`

 

Sample problems in trigonometry for learning final exam:

 

These are the sample problems solving by trigonometry terms. It is useful for learning final exam.

Problem 1:

What is the perimeter with radius 2.329 cm and central angle 263.54°?

Solution:
     Given angle = 263.54 * (3.14 / 180) = 4.599 radians.   

            Length of the arc s = rθ.                                    

                                     s = 2.329 * 4.5997                                  

                                     s = 10.71       

                     Perimeter = 2r + s                     

                                    = 2 * 2.329 + 10.712                     

                 Perimeter     = 15.37 cm.

Problem 2:

Prove that (1 + cos x) / sin x = sin x / (1 – cos x)

Proof: 
    RHS = sin x / (1 – cos x)   

  Taking conjugate to the above function        

            = [sin x / (1 – cos x)] * [(1 + cos x) / (1 + cos x)]        

            = sin x (1 + cos x) / (1 – cos2x)            

            = sin x (1 + cos x ) / sin2x           [ sin2x = 1 – cos2x]           

            = (1 + cos x) / sin x           

            = LHS.

Hence it is proved.