TEST - Trigonometry - March 2012

8/2/2019 TEST - Trigonometry - March 2012

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Integrated Math 2 Name ______________________Trigonometry Test Part 1 Date ___________ Block: _____You have about 35 minutes. Calculators are not permitted.

1) Determine the exact value of the following: 6 marks K

a) cos45o b) otan360 c) osin( 60 )

d) otan210 e) ocos( 90 ) f) osin510

2) Solve for, according to the given domain:

a) = o

2sin , 0 360

22 marks A

b) = o o

1cos , 180 540

22 marks A

2 marks T

c) = o otan 3, 0 360 2 marks A

3) Explain why the calculator gives you an error if you attempt to evaluate1sin (1.75)

1 mark C


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4) Given ocos140 0.766, find ocos40 . 1 mark T

5) The graph below has equation = +y cos(bx) d. Find the value ofb and d. 2 marks A

b = ______

d = ______

6) Point P (-3, 4) lies on the edge of this circle, forming an angle of with the

positivex-axis. Determine the sine, cosine, and tangent of. 4 marks T

a) sin = ______________

b) cos = _____________

c) tan = _____________

7) For the next problems, consider the graph siny x= (shown here) to be the parent function.

90 180 270 360

-3

-2

-1

xy


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-360 -270 -180 -90 90 180 270 360

-1

1

x

y

a) Graph

= 1

y sin x2 over the entire given domain. Clearly label (with coordinates) one

minimum value, one maximum value, and onex-intercept. 2 marks A2 marks C

b) For ( )= oy sin x 45 1, 4 marks K2 marks A

i) State the period: _________3 marks C

ii) State the amplitude: _________

iii) Describe the transformations fromy = sinx to this function: ____________

_____________________________________________________________

iv) Graph thefunction over

the entire given

domain:

Integrated Math 2 Name ______________________

-360 -270 -180 -90 90 180 270 360

-2

-1

1

2

x

y

-360 -270 -180 -90 90 180 270 360

-2

-1

1

2

x

y


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Trigonometry Test Part 2 Date ___________ Block: _____You have about 35 minutes. Calculators are permitted. If rounding is necessary, round to three significant

figures unless otherwise noted. Show all work!

Law of Sines:sin sin sinA B C

a b c= = Law of Cosines: Abccba cos2222 +=

1) A seven meter ladder is leaning against a building. The base of the ladder makes a 70 angle with

the ground. To the nearest hundredth, how far up the building does the ladder reach?

2 marks A

1 mark K1 mark C

2) Two aircraft leave the same airport, but flying in different directions. The angle between theirpaths is 35. After four hours, one aircraft has traveled 850 miles while the other has traveled 720

miles. Assuming they are at the same elevation, how far apart (to the nearest mile) are the aircraftat this time? Note: Draw and label a diagram of this situation as part of your solution.

2 marks A2 marks K

2 marks C

3) The height above the ground (in meters) of a rider on a Ferris wheel with a radius of 8 meters is

modeled by the equation = +h(t) 8sin(5(t 3)) 9, where t is measured in seconds. The graph of


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the function is shown below. Use the graph or the equation, along with your calculator and your

thinking skills, to answer the following questions. Estimated answers will be given no credit.

25 50 75 100 125 150 175 200

2

4

6

8

10

12

14

16

18

t

h

a) How long does it take for the wheel to make one revolution? 2 marks T

b) Find the height of the rider (to 3 s.f.) after 2 minutes. 3 marks A

c) At what times will the rider be farthest from the ground? 3 marks (Tech)

d) Find (to 3 s.f.) the first time the rider will reach a height of 12 meters. 3 marks A

4) Find the value ofx, to three significant figures. Show all working. 2 marks A2 marks K

1 mark C


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5) Find the missing values in the triangle below, rounding each value to the nearest whole number.

3 marks A

2 marks K 1 mark C

6) Solve 7 sin 2 5+ = for, for0 360 o o . Round your answers to the nearest degree.Make sure to give all relevant solutions.

4 marks T

Totals:Application: /27 Communication/Technology: /14

Knowledge: /17 Critical Thinking: /13

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TEST - Trigonometry - March 2012