Post on 11-Jan-2016
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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