Chapter 6:  Trigonometry, Trigonometric Functions and Its Applications

 

180 degrees = π radian

1 degree = (π/180) radian

1 radian = (180/ π) degrees

 

The Length of a Circular Arc

If an arc of length s on a circle of radius r subtends a central angle of radian measure θ, then

 

s = rθ

 

The Area of a Circular Sector

If θ is teh radian measure of a centrl angle of a circle of radius r and if A is the area of the circular sector determined by θ, then

 

A = (½)r2θ

 

1.      Find the radian measure:

a)     100°

b)     120°

c)      450°

      d)  - 300°

 

2.      Find the degree measure:

a)     2π/3

b)     2π

c)      π/9

d)     - π/2

 

3.      The tire of my 95 Eclipse is 26 inches in diameter.  If it is traveling at a speed of 90 miles/hour, find the number of revolutions the tire makes per minute.

 

Definition of the Trigonometric Functions

 

                    sinθ = opposite/hypotenuse      cscθ = hypotenuse/opposite

                   cosθ = adjacent/hypotenuse      secθ = hypotenuse/adjacent

                   tanθ = opposite/adjacent            cotθ = adjaent/opposite

 

Reciprocal Identities

                                     sinθ = 1/cscθ            cscθ = 1/sinθ

                                    cosθ = 1/secθ            secθ = 1/cosθ

                                     tanθ = 1/cotθ             cotθ = 1/tanθ

 

 

Verify the identities.

4.      cosθ secθ = 1

 

5.      (1 + cosθ)(1 - cosθ) = sin 2 θ

 

6.      cotθ + tanθ = cscθ secθ

 

7.      A survetor notes that the direction from point A to point B is S63°W and the direction from point to C is S38°W.  The distance from A to B is 239 yards, and the distance from B to C is 374 yards.  What is the distance from A to C?