Trigonometry Quizzes

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Trigonometry Quizzes

Quiz #1

Quiz #2

Quiz #3

Quiz #4

Quiz #5

Quiz #6

Quiz #7

Quiz #8

Quiz #9

Quiz #10

Quiz #11

Quiz #12

Quiz #13

Quiz #14

Quiz #15

Quiz #16

Quiz #17

Quiz #18

Quiz #19

Quiz #20

Quiz #21

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Definitions of TrigonometricValues of Acute Angles

of a Right Triangle

• For the triangle at the right …sin = __________cos = __________tan = __________cot = __________sec = __________csc = __________

a

b

c

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Definitions of TrigonometricValues of Acute Angles

of a Right Triangle

• For the triangle at the right …sin = __________cos = __________tan = __________cot = __________sec = __________csc = __________

a

b

c

acbcabbacbca

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Definitions of TrigonometricValues of Acute Angles

of a Right Triangle

• For the triangle at the right …sin = __________cos = __________tan = __________cot = __________sec = __________csc = __________

24

10

26

Simplify your answers by reducing any fractions!

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Definitions of TrigonometricValues of Acute Angles

of a Right Triangle

• For the triangle at the right …sin = __________cos = __________tan = __________cot = __________sec = __________csc = __________

24

10

26

Simplify your answers by reducing any fractions!

1213

513

125

512

135

1312

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Trigonometric Values of the Acute Angles of a Right Triangle.

Given that cot = 1.5, determine the following:

sin = ______

cos = ______

tan = ______

sec = ______

csc = ______

a

b

c

Hint: Let 1.5 = 3/2 and determine the values of a, b, and c in the diagram.

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Trigonometric Values of the Acute Angles of a Right Triangle.

Given that cot = 1.5, determine the following:

sin = ______

cos = ______

tan = ______

sec = ______

csc = ______

a

b

c

Hint: Let 1.5 = 3/2 and determine the values of a, b, and c in the diagram.

2 1321313

3 1331313

23

133

1323

213

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Trigonometric Values of the Acute Angles of a Right Triangle.

a = 6

b = 8

c = 10

--------------------

sin = ______

cos = ______

tan = ______

sec = 5

--------------------

sin = ______

cos = ______

tan = ______

cot = ______

csc = ______

a

b

c

Simplify your answers by reducing any fractions!

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Trigonometric Values of the Acute Angles of a Right Triangle.

a = 6

b = 8

c = 10

--------------------

sin = ______

cos = ______

tan = ______

sec = 5

--------------------

sin = ______

cos = ______

tan = ______

cot = ______

csc = ______

a

b

c

Simplify your answers by reducing any fractions!

35

45

34

24 2 661

1224

5 651224

2 6245 5

15

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Trigonometric Values of Special Angles

Complete the following table. Answers must be exact.

sin cos tan

0º

30º

45º

60º

90º

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Trigonometric Values of Special Angles

Complete the following table. Answers must be exact.

sin cos tan

0º

30º

45º

60º

90º

22

22

32

32

12

12

0

0

1

1

1

33

3

DNE

0

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Solve the Following Triangles(Use a calculator and round answers to 1 decimal place.)

A C

B

a

b

c

A = _________

B = _________

C = 90°

a = _________

b = 7

c = 10

A = 52°

B = _________

C = 90°

a = 17

b = _________

c = _________

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Solve the Following Triangles(Use a calculator and round answers to 1 decimal place.)

A C

B

a

b

c

A = _________

B = _________

C = 90°

a = _________

b = 7

c = 10

A = 52°

B = _________

C = 90°

a = 17

b = _________

c = _________

44.4

45.6

7.1

38

13.3

21.6

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45sin

30cos

60sec

90sin

0cos

30csc

30tan45tan

90cot45cot

Give exact answers. No calculators!

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45sin

30cos

60sec

90sin

0cos

30csc

30tan45tan

90cot45cot

Give exact answers. No calculators!

22

32

2

1

1

1

1

2

33

0

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AngleSmallest Positive Coterminal Angle

Reference Angle

582º

-260º

30sin

300cos

30tan

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AngleSmallest Positive Coterminal Angle

Reference Angle

582º

-260º

30sin

300cos

30tan

222

100

42

80

12

12

33

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AngleSmallest Positive Coterminal Angle

Reference Angle

200º

-300º

45sin

45cos

225tan

90sin

180cos

270tan

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AngleSmallest Positive Coterminal Angle

Reference Angle

200º

-300º

45sin

45cos

225tan

90sin

180cos

270tan

200

60

20

60

22

22

1

1

1

DNE

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AngleSmallest Positive Coterminal Angle

Reference Angle

3

11

4

3

Degrees 0º 30º 45º 60º 90º 150º

Radians

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AngleSmallest Positive Coterminal Angle

Reference Angle

3

11

4

3

Degrees 0º 30º 45º 60º 90º 150º

Radians

5

3

3

4

5

4

4

6

3

2

0

5

6

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1. Find the coterminal angle between 0 and 2 for each of the following:

-5/6 8/3

2. Find the reference angle (between 0 and /2) for each of the following:

3/4 5/6

3. Give the following trig values: sin(/6) = cos(3/4) = tan(-/3) =

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1. Find the coterminal angle between 0 and 2 for each of the following:

-5/6 8/3

2. Find the reference angle (between 0 and /2) for each of the following:

3/4 5/6

3. Give the following trig values: sin(/6) = cos(3/4) = tan(-/3) =

76

23

4

6

12

22

3

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3

4sin

6cos

4

3tan

sec 2

13csc

3

cot

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3

4sin

6cos

4

3tan

sec 2

13csc

3

cot

32

1

1

32

33

1

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3

sin

6

5cos

4

5tan

6

11sin

2cos

tan

4sin

3cos

6tan

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3

sin

6

5cos

4

5tan

6

11sin

2cos

tan

4sin

3cos

6tan

32

12

22

32

0

12

1

0

33

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Complete the following identities:

xsin

1 x

x

sin

cos

x

2tan

)cos( x )sin( x

)tan( x

x2sin1 x2sin21

xx 22 sincos xx 22 sincos

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Complete the following identities:

xsin

1 x

x

sin

cos

x

2tan

)cos( x )sin( x

)tan( x

x2sin1 x2sin21

xx 22 sincos xx 22 sincos

csc x

cos x

tan x

2cos x

1

cot x

sin x

cot x

cos 2x

cos 2x

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Function Domain Range

f(x) = sin-1x

g(x) = cos-1x

h(x) = tan-1x

2

1sin 1

2

1cos 1

2

1sin 1 1tan 1

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Function Domain Range

f(x) = sin-1x

g(x) = cos-1x

h(x) = tan-1x

2

1sin 1

2

1cos 1

2

1sin 1 1tan 1

, 2 2

0,

, 2 2

1, 1

1, 1

,

6

6

3

4

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2

3sin 1

2

3cos 1 1tan 1

2

1sin 1 0cos 1 0tan 1

2

2sin 1

2

1cos 1

3

3tan 1

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2

3sin 1

2

3cos 1 1tan 1

2

1sin 1 0cos 1 0tan 1

2

2sin 1

2

1cos 1

3

3tan 1

3

6

56

2

4

0

4

3

6

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2

3arcsin

2

3arccos 1arctan

2

1arcsin 0arccos 0arctan

2

2arcsin

2

1arccos

3

3arctan

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2

3arcsin

2

3arccos 1arctan

2

1arcsin 0arccos 0arctan

2

2arcsin

2

1arccos

3

3arctan

3

6

56

2

4

0

4

3

6

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1. State ONE of the Pythagorean identities.

2. State ONE of the double angle identities.

3. State ONE of the sum/difference identities.

4. Evaluate the following (exact answers without a calculator):

a. sin (7/6) =

b. arctan (-1) =

c. cos -1(-1/2) =

5. Evaluate the following (use a calculator and round to 2 decimal places):

a. csc (1.8) =

b. cot -1(5) =

c. arcsec (0.3) =

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1. State ONE of the Pythagorean identities.

2. State ONE of the double angle identities.

3. State ONE of the sum/difference identities.

4. Evaluate the following (exact answers without a calculator):

a. sin (7/6) =

b. arctan (-1) =

c. cos -1(-1/2) =

5. Evaluate the following (use a calculator and round to 2 decimal places):

a. csc (1.8) =

b. cot -1(5) =

c. arcsec (0.3) =

2 2cos sin 1x x

23

2 2cos(2 ) cos sinx x x

cos( ) cos cos sin sina b a b a b

4

12

1.03

0.20

DNE

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0sin 1

0cos 1

0tan 1

2

3sin 1

2

2cos 1

3tan 1

))25.0(sin(sin 1

)2cos(cos 1

4sincos 1

7

1cossin 1

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0sin 1

0cos 1

0tan 1

2

3sin 1

2

2cos 1

3tan 1

))25.0(sin(sin 1

)2cos(cos 1

4sincos 1

7

1cossin 1

0

2

0

3

34

3

0.25

DNE

34

48 4 37 7

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1sin 1

1cos 1

1tan 1

2

2sin 1

2

3cos 1

3tan 1

))5.0(tan(tan 1

)3sin(sin 1

4sincos 1

5

3sincos 1

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1sin 1

1cos 1

1tan 1

2

2sin 1

2

3cos 1

3tan 1

))5.0(tan(tan 1

)3sin(sin 1

4sincos 1

5

3sincos 1

2

4

4

6

3

0.5

DNE

4

45

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Convert from Polar to Cartesian:

(0, 120º) = (___, ___)

(7, -45º) = (___, ___)

r = 3sin - 4cos __________________

Convert from Cartesian to Polar:

(0, 12) = (___, ___º)

(7, -7) = (___, ___º)

2xy = 1 __________________

Determine the Polar coordinates for the point (-5, 200º) that satisfies the following criteria:

r > 0 & 0º < < 360º (___, ___º)

r < 0 & -360º < < 0º (___, ___º)

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Convert from Polar to Cartesian:

(0, 120º) = (___, ___)

(7, -45º) = (___, ___)

r = 3sin - 4cos __________________

Convert from Cartesian to Polar:

(0, 12) = (___, ___º)

(7, -7) = (___, ___º)

2xy = 1 __________________

Determine the Polar coordinates for the point (-5, 200º) that satisfies the following criteria:

r > 0 & 0º < < 360º (___, ___º)

r < 0 & -360º < < 0º (___, ___º)

5, 20

5, 160

0, 0

7 2 7 2, 2 2

2 2 3 4x y y x

12, 0

7, 45 7, 315

csc(2 )r