Math Assignment (homework)

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

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.

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

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