1. Trigonometry Stations
Chapter 9
Trigonometry Stations

2. Name ________________
Honors Chapter 9 Stations Review
Name ________________
#1 A. ___
B. ___
C. ___
D. ___
E. ___
#2 A. B.
#3 A. #4 #5
sin θ = __________ csc θ = _________
cos θ = __________ sec θ = _________
tan θ = __________ cot θ = _________ #6

3. #7 A. #8 #99 #10 #119 #12 Amplitude: A. Period: B. B. Amplitude: C. A.

4. #1 Column A Column B A. tan A I. 𝑏 𝑐 B. cos A II. 𝑝 𝑞 C. sin P
Match each trigonometric concept found in Column A with the correct ratio found in Column B. A B C a b c q Q R P p r
Column A
Column B
A. tan A
I. 𝑏 𝑐
B. cos A
II. 𝑝 𝑞
C. sin P
III. 𝑞 𝑟
D. cot P
IV. 𝑟 𝑝
E. sec P
V. 𝑎 𝑏

5. #2
A man stands at a distance of 8 meters from a lamppost. When standing as shown, he measures the angle of elevation as 34. Find the height of the lamppost.
A radar operator notes that an airplane is at a distance of 2000 meters and at a height of 800 meters. Find the angle of elevation.

6. #3 #4 Simplify the following. 𝑠𝑒𝑐𝜃− sin 𝜃 tan 𝜃 𝑠𝑒𝑐θ 𝑐𝑜𝑡𝜃+𝑡𝑎𝑛𝜃
The diagram shows a crane working on a wharf. AB is vertical. Find the measure of angle ABC.

7. #5
Let (-7, 24) be a point on the terminal side of an angle in standard position. Evaluate the six trigonometric functions of the angle.
sin θ = ___________ csc θ = ___________
cos θ = ___________ sec θ = ___________
tan θ = ___________ cot θ = ___________
(-7, 24) #6
A person standing on the earth notices that a 747 Jumbo Jet flying overhead subtends an angle of 0.45°. If the length of the jet is 230 feet, find its altitude to the nearest thousand feet.

8. #6
A child is on a swing in a park. The highest position that she reaches is as shown. Find the height of the swing seat above the ground in this position.
B. A flag pole is fixed to a wall and supported by a rope, as shown. Find the angle between the pole and the wall.

9. #7 #8 Verify the following identities.
𝑡𝑎𝑛 2 𝜃 𝑐𝑜𝑠 2 𝜃+ 𝑐𝑜𝑡 2 𝜃 𝑠𝑖𝑛 2 𝜃=1
𝑐𝑜𝑠 2 𝜃 −𝑠𝑖𝑛 2 𝜃 1− 𝑡𝑎𝑛 2 𝜃 = 𝑐𝑜𝑠 2 𝜃 #8
The angles of elevation of a hot air balloon from two points, A and B, on level ground, are 24.2 and 46.8 respectively. The points A and B are 8.4 miles apart, and the balloon is between the points in the same vertical plane. Find the height of the balloon above the ground.

10. #9 #10 Find the angle’s reference angle.
a. −140° b. 14𝜋 c. 3𝜋 4
#10
Find the amplitude and period of the graph of the function.
a. 𝑔 𝑥 =3 sin 𝑥 b. 𝑔 𝑥 =4 cos 𝜋𝑥

11. #12
Write an equation of the form y=a sin b x−h +k or y=a cos b x−h +k, so that the graph has the given amplitude, period, vertical shift, and horizontal shift.
a. amplitude: b. amplitude: 1/2
period: period: 3𝜋 , vertical shift: vertical shift: -5
horizontal shift: 𝜋 horizontal shift: 0
function: sin x function: cos x
#11
A lawn sprinkler located at the corner of a yard is set to rotate through 90 degrees and project water out 30 feet. To three significant digits, what area of lawn is watered by the sprinkler?

12. Additional problems

13. #5
Write a short story with a problem situation based on what you see in the illustration below. Include the solution to the problem you wrote.
37°
22 m
18 m x

14. #9
The diagram below consists of 3 triangles - ∆𝑋𝑌𝑍, ∆WYZ, and ∆WZX. Angles are denoted by upper case letters and lengths by lower case letters. In the allotted time, make as many true statements of equality as you can about this diagram. Your statements should therefore all be equations.

15. #10
Write a short story with a problem situation based on what you see in the illustration below. Include the solution to the problem you wrote.
200𝑚
80°
55°