Algebra 2/Trig Final Exam STUDY GUIDE Mrs. Grieser

[Pages:8]Algebra 2/Trig Final Exam STUDY GUIDE

Mrs. Grieser

Name: _______________________________________ Date: ________________ Block: __________

Algebra 2/Trig Final Exam STUDY GUIDE The final exam covers the trigonometry portion of the course, including:

Find trig ratios in a right triangle; solve right triangles. Find arc sector lengths and areas in radians Find the six trig ratios relative to a given point on a circle. Given one trig function value, find the value of the other five trig functions. Know the trig values of angles found on the unit circle (know the unit circle!). Convert angles from degrees to radians or radians to degrees. Given an angle in degrees or radians, find coterminal angles. Find the value of any trig function or inverse trig function. Know the domain of inverse trig functions. Verify trig identities, or use trig identities to simplify trig expressions. Find the exact value of a trig function by using sum or differences of angles, half

angle formulas, or double angle formulas. Know the domain and range of the trig functions in standard form, and be able to use

transformations to graph trig functions, including finding amplitude (sine and cosine), period, phase shift, vertical displacement, and asymptotes (if applicable). Solve trigonometric equations, either for a general solution, or for a solution on a given interval. Apply the law of cosines or sines to solve triangles or word problems involving triangles. DO NOT LIMIT STUDYING TO QUESTIONS ON THIS GUIDE. Use old study guides, tests, checkpoints, and other material for topics you need more practice with. Practice Questions: 1) Find the exact values of the expressions without using a calculator:

a) cos165

b) tan 60

c) sin15

d) sin 7 8

e) tan11 12

f) cos 12

Algebra 2/Trig Final Exam STUDY GUIDE

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2) a) Find the arc length of a sector with radius 8 feet and a central angle of 60 .

b) Find the area of the sector described in the previous question.

3) a) Write two x-values at which the function f (x) 4cos 2x has a maximum. b) Find the amplitude and period of the function in the previous question.

4) Graph y 2 tan x . Include vertical asymptotes in your sketch. What is the amplitude and period of the graph?

5) Sketch the graph of f (x) 3sin x . What is the amplitude and period of the graph? 2

Algebra 2/Trig Final Exam STUDY GUIDE

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6) Write an equation of the form y a sin bx , where a>0 and b>0, with amplitude 2 and 3

period 12.

7) Find sinA B given that sin A 6 with A and cos B 2 with B 0 .

7

2

5

2

8) Find the general solution of the equations, unless an interval is given.

a) 12 tan2 x 4

b) cos x tan x cos x

c) cos 2x cos x

d) 2sin2 x sin x 1 0 on 0 x 2

e) sin 2x cos x sin x on 0 x 2

f) cos2 xsin x 5sin x on 0 x 2

9) Convert degrees to radians, or radians to degrees:

a) 48

b) 245

c) 5 9

d) 9 10

10) You are flying a kite and want to know its angle of elevation. The string on the kite is 31 meters long and the kite is level with the top of a building that you know is 21 meters high. Find the angle of elevation of the kite.

11) Find x to the nearest hundredth.

12) Solve for x to the nearest degree.

Algebra 2/Trig Final Exam STUDY GUIDE

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13)Write the equation of the resulting graph when y 1 cos 3 x is translated two units to 58

the left.

14)Write the equation of the resulting graph when y 6sin x is translated up two units. 3

What is the amplitude and period of the resulting graph after the translation?

15) A slide 3.5 m long makes an angle of 28 with the ground. How high is the top of the slide above the ground?

16) Simplify the expressions.

a) sin x 5 2

b) csc x cos(x)

c) sin xsec x 2

d) cos 2 x cos 2 (x) 2

e) (sec x 1)(sec x 1) tan x

f) tan x cot x csc2 x 2

17)If cos 1 and terminates in the first quadrant, find the exact value of sin 2 . 2

18)Given sin 2 , where 0 , find the value of sin 2 . Round the answer to three

15

2

decimal places.

19)Find the amplitude and period of the graph y 3cosx .

20) The point (?3, 3) is on the terminal side of an angle . Find the six trigonometric function values of .

Algebra 2/Trig Final Exam STUDY GUIDE

21)Solve tan 3.2 on 180 270 .

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22)Which of the angles are coterminal? , 3 , 7 44 4

23)Find one positive angle and one negative angle that are co-terminal with 124 .

24)Find one positive angle and one negative angle that are co-terminal with 3 . 8

25)Evaluate the six trigonometric functions of 4 3

26) Verify the identities. SHOW ALL STEPS. a) cos(x) sec x tan x

1 sin(x)

b)

cos 2 x sin 2 tan2 x 1

x

cos 2

x

c) 2 sec2 x 1 tan2 x

d) sin x cos x cot x csc x

Algebra 2/Trig Final Exam STUDY GUIDE

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27) Solve ABC given the values. Round to the nearest tenth if necessary.

a) a 12, b 19, c 21

b) A 51, B 50, b 74

c) A 34, C 90, a 19

d) A 50, b 9, c 7

e) C 98, c 29, a 33

f) B 21, b 17, c 32

28) A surveyor wants to find the width of a river from a particular point on the shoreline for construction of a bridge. The surveyor's measurements are shown in the figure. How wide is the river?

Algebra 2/Trig Final Exam STUDY GUIDE

STUDY GUIDE ANSWERS

1) Note: for some answers, other correct forms may exist

a)

2

6

b)

3

c)

6 2 d)

2 2 e) 2 3 f)

2 6

4

4

2

4

2) a) s 8 ft b) A 32 ft2

3

3

3) a) 0, (there are other correct values) b) amplitude: 4, period:

4) no amplitude, period:

5) amplitude: 3,

period: 4

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6) y 2 sin x 36

7) 12 273 35

8)

a)

n , 5 n

b)

n c)

2 2 n,

4 2 n,

2n d)

7 11 , , e)

0, , 3 , , 5 , 7

6

6

4

3

3

26 6

44 4 4

f) 0,

9)

4

a) b)

49

c) 100

d) 162

15 36

10) 42.64

11) 10.07

12) 48

13) y 1 cos 3 x 2

58

14) y 6sin x 2 ; amplitude 6; period: 6 3

15) 1.64 m

16)a) cos x b) cot x c) 1 d) 1 e) tan x f)-1

17) 3 2

18) 0.264 19) amplitude: 3; period: 2

20) sin 2 , cos 2 , tan 1, csc 2,sec 2, cot 1

2

2

21) 253

22)

and

7

4

4

23) 484, 236 (there are other correct answers)

Algebra 2/Trig Final Exam STUDY GUIDE

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13

24) ,

19

(there are other correct answers)

8

8

25) sin 3 , cos 1 , tan 3, csc 2 3 ,sec 2, cot 3

2

2

3

3

cos(x) cos x cos x(1 sin x) cos x cos x sin x cos x cos x sin x 1 sin x

26) a)

1 sin(x) 1 sin x

1 sin2 x

cos 2 x

cos 2 x

cos 2 x

sec x tan x

cos x cos x

b) cos 2 x sin 2 x 1 cos 2 x c) 2 sec2 x 2 (tan2 x 1) 2 tan2 x 1 1 tan2 x tan2 x 1 sec2 x

d) sin x cos x cot x sin x cos x cos x sin x cos2 x sin 2 x cos2 x 1 csc x

sin x

sin x

sin x

sin x

27)a) A 34.5, B 63.6, C 81.9 b) C 79, a 75.1, c 94.8 c) B 56, b 28.17, c 33.98

d) a 7, B 80, C 50

e) no triangle

f) A 116.6, C 42.4, a 42.4; A 21.4, C 137.6, a 17.3

28) about 55.5 ft

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