Download ch 4 Practice test by claims

Chapter 4 Practice Test
Right Triangle Trigonometry and Circular Functions
Choose 18 problems to do making sure to do at least one for each of the
claims (sections).
Claim #1 – Concepts and Procedures
13
r
1. Convert the angles measures:
a. 216 
b.
23
15
2. Find the values of the 6 trig functions of the angle Be exact.
35

3. Use a calculator to evaluate the following. Round your answer to the hundredths place, if needed.
- 9
a. sin 12 
b. tan
c. cot (-27 )
d. cos   -0.3
4
For questions 4 -6, evaluate the following trig functions exactly by hand.
4

4. tan 135 
5. cos
6. tan (-7  )
3
For questions 7 – 9, create a labeled graph of the trig functions. Include at least 2 periods.
x
7. y = 4 cos(x)
8. y = -5csc  
9. y = 4 tan(2x)
4
 2

For questions 10– 11, find the exact values by hand. 10. sin 1 

2


11. cos11
Claim #2– Problem Solving
12. Multiple Choice: Bob the Builder uses a 20 foot ladder to paint a section of his house that is 16 feet high.
Select all equations that can be used to solve for θ. Then, solve one of the chosen equations to find θ.
16
20
12
12
a.) sin  
b.) csc  
c.) tan  
d.) cot  
20
12
20
16
Ones that Work:_______________ Solution θ=______
13. Callihan drew a right triangle. The length of the hypotenuse in each triangle is 180 units. The perimeter
of Callihan’s triangle is 18+ 180 units. Determine the dimensions of his triangle.
14. Consider right triangle ABC, where angle C is a right angle. Place each measure of angle A into the column
that makes the relationship between sin A and cos A true.
Angle A Measurements to Place:
18◦, 23◦, 36◦, 48◦, 81◦, and 89◦
cos A < sin A
cos A = sin A
cos A > sin A
15. Consider this situation: Bobby places his surveyor’s telescope on top of a tripod that is 7 feet above the
ground. He then measures a 12 angle of elevation above the horizontal to the top of a lighthouse which is 135
feet away. He wants to find the height of the lighthouse to the nearest foot. Include a diagram and the trig.
equation you use.
16. A ramp leading to a freeway overpass is 400 ft long and rises 64 feet. What is the angle of inclination of
the ramp to the nearest tenth of a degree?
Claim #3 – Communicating Reasoning
17. Consider this right triangle. Determine whether each equation is correct. Select Yes or NO for each
equation. Then, explain why the ones marked no are wrong.
4
4
4
sin B 
cos B 
tan B 
5
5
5
18. Multiple Choice: Using a calculator, determine which of the following does not represent a real number.
 3
Then explain how you know. a. sin 45
b. csc 90
c. cos 
d. sec
2
19. Know the lyrics to the trig. song. (Hint: I was walking through the forest…)
20. What is the difference between negative and positive angles? Be specific.
21. Arthur was solving a problem involving cotangent. He got confused as to whether he should use the
reciprocal of tangent or the inverse of it? Which should he use? If neither of these should be used, explain
what he should do.
22. Multiple Choice: Which of the following is true for y = 17tan(4x)? Justify your answer.
a. the period is 180  and the amp. is unimportant.
b. the period is unimportant and the amp.is 90 
c. the period is 
4
and the amp. is unimportant
d. the period is unimportant and the amp. is 
3
23. Do all trig functions have inverses? Are all of the inverses functions? Why or why not?
Claim #4 – Modeling and Data Analysis
24. Farmer Fanny is building 4 new grain bins which can be used to store the harvested corn. A leg elevator,
which moves the corn from the ground level into the bins, must also be built. See the pictures below if you
need a visual.
Fanny hires a local engineer who drafts some Grain Bin Specifications (see below). But, before he finishes the
work, he gets called away on an emergency project for the city, leaving Fanny with an incomplete project.
Fanny thinks she has enough information to give to the project manager to start construction.
Fanny’s Grain Bin Specifications:
 The bins are 18 feet tall not including the cap
 The cap of each bin forms a 35◦ angle with the base of the bin
 The distance from the outer edge of the bins to the leg elevator will be 20 feet
 The distance from the inner edge of the bins to the leg elevator will be 7 feet
 A gravity spout is placed so that it runs from the top of the cap to a point that is 4 feet below the top of
the elevator leg. To account for certain moisture content the gravity spouts will slope 40 degrees to the
horizontal.
Your task
i.) Label the dimensions on the diagram based on the Grain Bin Specifications
x
ii.) Set up and solve a trigonometric equation that can be used to solve for y
y
iii.) Set up and solve a trigonometric equation that can be used to solve for x
iv.) How tall will her Grain Bins be including the cap?