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Mathematics 5

ANSWERS Review worksheet 5


1.  Convert the following:
a)  131° to radians.

180° = pi radians
1      = pi / 180

131 = 131pi / 180
b)  17pi / 3 to degrees.

180° = pi radians
(17 / 3)(180) = (17 / 3)(pi)
1020 = 17pi / 3

c)  1.42 radians to degrees.

180° = pi radians
180 / pi = 1
(1.42)(180 / pi ) = (1.42)(1)

(142 / 100 )(180 / pi ) = 1.42
1278 / 5 pi = 1.42
 


2.  The point (-6, 2) lies on the terminal arm of an angle.
      Give the 6 trig ratios of this angle.  (Do NOT calculate the measure of the angle).

the six trig ratios can be expressed in terms of x, y, and r.  we know x and y, we need to find r.
Let A be the angle.

r2 = x2  + y2
r2  = (-6)2  + (2)2
r2  = 36 + 4
r2  = 40
r = SQRT(40)
4 = 2SQRT(10)
r = 6.32

sinA = y / r
sin A = 2 / 2SQRT(10)
sin A = 1 / SQRT(10)
sin A = SQRT(10) / 10

cosA = x / r
cosA = -6 / 2SQRT(10)

cosA = -3SQRT(10) / 10

tanA = y / x
tanA = 2 / -6
tanA = -1 / 3

cscA = 1 / sin A
cscA = SQRT(10)

secA = 1 / cosA
secA = -SQRT(10) / 3

cotA = 1 / tanA
cotA = -3
 
 


3.  A horse is inside a large rectangular field.  The horse is tied with a 20 foot rope to the fence, 15 feet from a corner of the field.  What is the area that the horse is free to move about in?

Draw a diagram.  Then check  here  to see if your diagram is accurate.

From the diagram we have two shapes to calculate, a triangle and a sector.

For the triangle,
cos A = a / h
cosA = 15 / 20
A = 0.723 radians.

Area (triangle) = absinC / 2
Area = (15)(20)sin(0.723) / 2
Area = 99.2

Since the angle in the triangle is 0.723, the angle of the sector is pi - 0.723 = 2.419

Area (sector) = r2 theta / 2
Area = (20)2 (2.419) / 2
Area = 483.8

Total Area = Area (triangle) + Area (sector)
                    = 99.2 + 483.8
                    = 583 m2
 
 


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