Math Assignment (homework)

Help me for math

CanSTEM Education Private School Inc.

20-MCR3U Functions Grade 11 Trigonometry Unit-3 Chapter–5-6 Unit Test
Name:__________________ Teacher: Sajjala P. Sankhe Date:__________ Marks:_____ /50

Instruction: Use separate answer sheet for answers. Attach with Question set. Show all work. Be neat and clear. Write conclusions for all word problems.

Exam is in two part. Part-A—50 Marks. Part-B—50 Marks.

Teacher Remarks/Comments:

Part-A

/10 ku

/15 app

/15 tips

/10 comm

Knowledge and Understanding

1.Determine all values of, to the nearest degree, if 0 360.[K/U=4][C=4]
a) tan = b) csc = – 3.5

2.The point (3, – 6) lies on the terminal arm of an angle in standard position.
a) Sketch the principal angle [K/U=2] B) Find the six trigonometric ratios. [C=2]

C) What is the value of the principal angle , to the nearest degree? [K/U=2]

3. Solve each triangle. Calculate all side lengths to the nearest tenth and all interior angles to the nearest degree, where appropriate. Show all work and include a diagram. [K/U=2][C=4]
a) ∆XYZ, where ∠X = 30, x = 7.5 cm, y = 15 cm.
b) ∆ KMN, where ∠K = 54o, m = 6.2 cm, k = 4.8 cm.
D) ∆PRQ, where ∠P = 34, p = 3.9 cm, r = 6.2 cm.

Application

4.A guy wire supporting a telephone pole is secured to the ground at a point 16.7 m from the base of the pole. The wire makes an angle of 48 with the ground. Find the length of the wire, to the nearest tenth of a meter, using a reciprocal trigonometric ratio. Include a diagram. [4]
Solution

5.Given: cos = – sin < 0 a) In which quadrant does the terminal arm lie? [2] b) Determine the following trigonometric ratios: tan and csc . [2] 6.A light in a park can illuminate effectively up to distance of 175 m. A point on a bike path is 350 m from the light. The sight line to the light makes an angle of with the bike path. What length of bike path, to the nearest meter, is effectively illuminated by the light?[3] 7. Prove each of the following identities. Show all work! a) sec2 + csc2 = sec2csc2 [2] b) + = 2cot csc. [2] Thinking 8. Given sincot = determine. [5] 9.A marathon swimmer starts at at Island A, swims 9.2 km to Island B, then 8.6 km to Island C. The angle formed by a line from Island B to Island A and a line from Island C to Iland A is 52. How far does the swimmer have to swim to return directly to Iland A. Include a diagram. [5] 10. Prove the following identity. Show all the steps of your solution. [5] = 1 + cot . Part-B: Show all work. Be neat and clear. Write conclusions for all word problems. /10 ku /15 app /15 tips /10 comm Knowledge 1. Prove the following [8 marks each] a. sin csc + cos sec = 2 b. = sin c. tan2 – sin2 = tan2 sin2 [2] Communication 2. Solve the following for 0ox 360o [8] a. 2cos x = – b. 3sin x+ 3 = sin x + 2 Application (15 marks) 3. Solve the following for 0ox 360o [2 marks] a)– 3 cos x+ 3 = 2 sin2x b) cos x = , [2] c) cos x = 1, x = 0o or x = 360o.[2] 4. Prove the following: [3 marks each] a. (sin – tan ) (cos – cot ) = (sin – 1) (cos – 1) b. = c. = Thinking and Inquiry 5. Solve the following for 0ox 720o [3 marks each] 1. cos = – 1 b. 2 cos x sin x + 2 cos x – sin x – 1 = 0 [6] 1) sin x = – 1, x = 270o or x = 270o + 360o = 630o. 2) cos x = 6. Prove the following [6] 1 + tan2= sec2 1 + cot2= csc2 a. csc4– cot4 = csc2 + cot2 b. – = 4 tan sec Property of CanSTEM Education Private School Inc. 2017-2018 Page No. 4

CanSTEM Education Private School Inc.

12-MCR3U Functions A as L Trigonometry Unit 3 Chapter-6 Quiz-2
Name:_________ _____ Date:_____________ Teacher: Sajjala P. Sankhe Marks:_______/10

Instruction: Use separate answer sheet and Graph paper, where and if needed. Attach them with question set properly and mark question number and unit/chapter no. on answer sheet.
At an amusement park, Ms. Smith had different students ride two Ferris wheels. John rode on Ferris wheel A, and Laura rode on Ferris wheel B. Ms. Smith collected data and produced two graphs.

1. What information about the Ferris wheels can you learn from the graphs of these functions?
2. Find the Period and the Number of Cycles in the Period for Graph A & Graph B.
3. Find the Equation of Axis of the Curve for Graph A & Graph B. Find the Amplitude for Graph A & Graph B.
4. Find the Equation of Sinusoidal Function for Graph A & Graph B.
5. Calculate and Comparing Speeds in Sinusoidal Functions. Who is travelling faster: John or Laura?
s =

Property of CanSTEM Education Private School Inc. 2017-2018 Page No. 1

CanSTEM Education Private School Inc.

1-1-MCR3U Functions-11 A for L Unit—3 Chapter-5 Sine & Cosine Law Assignment
Name:_________________ Date:____________ Teacher: Sajjala P. Sankhe Marks:_____/100

ku /20%

app /30%

tips /30%

comm /20%

Instruction: Use separate answer sheet for answers, where needed. Attach them with Question set. Show all work. Include a diagram.

Teacher Remarks/Comments:

Categories

50−59% (Level 1)

60−69% (Level 2)

70−79% (Level 3)

80−100% (Level 4)

Knowledge and Understanding – Subject-specific content acquired in each course (knowledge), and the comprehension of its meaning and significance (understanding)

The student:

Knowledge of content (e.g., facts, terms, procedural skills, use of tools)

demonstrates limited knowledge of content

demonstrates some knowledge of content

demonstrates some knowledge of content

demonstrates thorough knowledge of content

demonstrates thorough knowledge of content

demonstrates limited understanding of concepts

demonstrates some understanding of concepts

demonstrates considerable understanding of concepts

demonstrates thorough understanding of concepts

Thinking – The use of critical and creative thinking skills and/or processes*

The student:

Use of planning skills − understanding the problem (e.g., formulating and interpreting the problem, making conjectures) − making a plan for solving the problem

uses planning skills with limited effectiveness

uses planning skills with some effectiveness

uses planning skills with considerable effectiveness

uses planning skills with a high degree of effectiveness

Use of processing skills − carrying out a plan (e.g., collecting data, questioning, testing, revising, modelling, solving, inferring, forming conclusions) − looking back at the solution (e.g., evaluating reasonableness, making convincing arguments, reasoning, justifying, proving, reflecting)

uses processing skills with limited effectiveness

uses processing skills with some effectiveness

uses processing skills with considerable effectiveness

uses processing skills with a high degree of effectiveness

Use of critical/creative thinking processes (e.g., problem solving, inquiry)

uses critical/ creative thinking processes with limited effectiveness

uses critical/ creative thinking processes with some effectiveness

uses critical/ creative thinking processes with considerable effectiveness

uses critical/ creative thinking processes with a high degree of effectiveness

Communication – The conveying of meaning through various forms

The student:

Expression and organization of ideas and mathematical thinking (e.g., clarity of expression, logical organization), using oral, visual, and written forms (e.g., pictorial, graphic, dynamic, numeric, algebraic forms; concrete materials)

expresses and organizes mathematical thinking with limited effectiveness

expresses and organizes mathematical thinking with some effectiveness

expresses and organizes mathematical thinking with considerable effectiveness

expresses and organizes mathematical thinking with a high degree of effectiveness

Communication for different audiences (e.g., peers, teachers) and purposes (e.g., to present data, justify a solution, express a mathematical argument) in oral, visual, and written forms

Communication for different audiences (e.g., peers, teachers) and purposes (e.g., to present data, justify a solution, express a mathematical argument) in oral, visual, and written forms

communicates for different audiences and purposes with some effectiveness

communicates for different audiences and purposes with considerable effectiveness

communicates for different audiences and purposes with a high degree of effectiveness

Use of conventions, vocabulary, and terminology of the discipline (e.g., terms, symbols) in oral, visual, and written forms

uses conventions, vocabulary, and terminology of the discipline with limited effectiveness

uses conventions, vocabulary, and terminology of the discipline with some effectiveness

uses conventions, vocabulary, and terminology of the discipline with considerable effectiveness

uses conventions, vocabulary, and terminology of the discipline with a high degree of effectiveness

Application – The use of knowledge and skills to make connections within and between various contexts

The student:

Application of knowledge and skills in familiar contexts

Application of knowledge and skills in familiar contexts

Application of knowledge and skills in familiar contexts

Application of knowledge and skills in familiar contexts

applies knowledge and skills in familiar contexts with a high degree of effectiveness

applies knowledge and skills in familiar contexts with a high degree of effectiveness

applies knowledge and skills in familiar contexts with a high degree of effectiveness

applies knowledge and skills in familiar contexts with a high degree of effectiveness

transfers knowledge and skills to new contexts with considerable effectiveness

transfers knowledge and skills to new contexts with a high degree of effectiveness

transfers knowledge and skills to new contexts with a high degree of effectiveness

transfers knowledge and skills to new contexts with a high degree of effectiveness

makes connections within and between various contexts with some effectiveness

makes connections within and between various contexts with considerable effectiveness

makes connections within and between various contexts with a high degree of effectiveness

1. Given that,, and , how many triangles are possible?
a) 0 triangles b) 1 triangle c) 2 triangles d) 3 triangles
2. Find the measure of the angle A in a triangle ABC if AB = 4.8 cm, BC = 4.1 cm, and AC = 6.7 cm. Round your answer to the nearest degree.
3. Solve Δ ABC if AB = 11 cm, AC = 9 cm, and ∠B = 48o. [A 3]

4. A crow sitting on the top of a tree with a piece of cheese in her beak sees a fox and a wolf in the same line of sight, the fox is 10 m ahead of the wolf. The crow is 70 m from the fox and observes the wolf at the angle of depression of 16o. Determine the angle of depression the crow observes the fox and the height of the tree. [T 3]
Solution

5. From one side of a river, John sees two trees on the opposite side. The distances from John to the trees are 50 m and 35 m, and the angle between the two trees from John’s perspective, is 67o. How far apart are the trees, to the nearest centimetre? Include a labelled diagram in your solution. [A 3] [C 1]
6. A boat is approaching a cliff which is 50 m tall. If the angle of elevation from the boat is, how far away is the boat from the cliff? Give the exact value, not an approximation. [APP ]
7. Find x in the diagram. [K/U ]

8. In ABC, a = 6, b = 16, ∠C = 60. Find [K/U]
9. Solve each triangle. Calculate all side lengths to the nearest tenth and all interior angles to the nearest degree, where appropriate. Show all work and include a diagram. [8]
a) ∆XYZ, where ∠X = 30, x = 7.5 cm, y = 15 cm.

b) ∆ KMN, where ∠K = 54o, m = 6.2 cm, k = 4.8 cm.

a) ∆PRQ, where ∠P = 34, p = 3.9 cm, r = 6.2 cm.

10. A marathon swimmer starts at at Island A, swims 9.2 km to Island B, then 8.6 km to Island C. The angle formed by a line from Island B to Island A and a line from Island C to Iland A is 52. How far does the swimmer have to swim to return directly to Iland A. Include a diagram. [4]

11. In ABC, ∠A = 51, a = 12 cm, and b = 15 cm. Solve the triangle. Include a diagram. Round all angles to the nearest degree and sides to the nearest tenth of a centimetre. [4]

Application

12. From a position some distance away from the base of a flagpole, Justin estimates that the pole is 4.25 m tall at an angle of elevation of 35. If Justin is 1.65 m tall, use a reciprocal trigonometric ratio to calculate how far he is from the base of flagpole, to the nearest hundredth of a meter. Include a diagram. [3]

13. From a window in a building, the angle of depression to a parked car is 32. From a window that is 12 m lower, the angle of depression to the parked car is 21. How far is the parked car from the base of the building, to the nearest metre? Include a diagram. [3]

14. Given PQR, QR = 5.6 m and S is the midpoint of QR. Determine PQ, to the nearest tenth, if ∠PSQ = 33 and ∠ PRQ = 22. Include a diagram. [3]

15. Explain when an ambiguous case might exist. Include all necessary conditions. As part of your explanation, provide examples (including a diagram) of possible given value that would result in an ambiguous case. You do not need to solve your own examples. [6C]

Application [12 Marks]

16. Emma is on a 50 m high bridge and sees two boats in the water below her. Emma estimates the angles of depression to be 38 for boat A and 35 for boat B. How far apart are the two boats if the angle in between Emma’s lines of sight of the two boats is l10. Draw a diagram as part of your solution.
Solution

17. A plane’s route is passing above Sinville and Tangland. The plane is 6.7 km directly away from Sinville and 5.3 km directly away from Tangland. The angle of elevation from Sinville to the plane is 42. How far apart are Sinville and Tangland? Draw a diagram and consider al1possibilities.

Property of CanSTEM Education Private School Inc. 2017-2018 Page No. 1

CanSTEM Education Private School Inc.

11-MCR3U Functions A as L Trigonometry Unit 3 Chapter-6 Quiz -1
Name:_________________ Date:___________ Teacher: Sajjala P. Sankhe Marks: _____/ 30

Instruction: Use separate answer sheet and Graph paper, where and if needed. Attach them with question set properly and mark question number and unit/chapter no. on answer sheet.

Example 1 Determine if the function is periodic. If so, state the period, the maximum value, the minimum value and the amplitude.

d) Tip of vibrating meter stick

e) Movement of a piston in a combustion engine

Knowledge and Understanding
1. State whether each of the following graphs represents a periodic function or not. [3 marks]
a)

b)

c)

2. State the period and amplitude of each of the following functions. [4 marks]
a)

b)

Property of CanSTEM Education Private School Inc. 2017-2018 Page No. 3