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QUESTION
ANSWER
Clever Catch®
62.
What is the length of the longer side in a 30˚-60˚ right triangle with a hypotenuse length of
2?
63.
Solve for θ in standard position with 90˚ ≤ θ ≤ 180˚ if sin θ = 1/2.
64.
Solve for θ in standard position with 180˚ ≤ θ ≤ 360˚ if tan θ = - 1
315˚
65.
Solve for θ in standard position with 0˚ ≤ θ ≤ 180˚ if cos θ = -
135˚
66.
Solve for θ in standard position with 180˚ ≤ θ ≤ 360˚ if sec θ is undefined.
270˚
67.
Find the degree measure for an angle with 4π/3 radian measure.
240˚
68.
Find the degree measure for an angle with 5π/6 radian measure.
150˚
69.
Find the radian measure for an angle with 135˚ measure.
3π/4
70.
Identify the trigonometric function which can be defined in terms of the ratio: (side
opposite)/hypotenuse
Sine
71.
Identify the trigonometric function which can be defined in terms of the ratio: hypotenuse/ Cosecant
(side opposite)
72.
Identify the trigonometric function which can be defined in terms of the ratio: (side
adjacent)/hypotenuse
73.
Identify the trigonometric function which can be defined in terms of the ratio: hypotenuse/ Secant
(side adjacent)
BASIC PLAY:
74.
Identify the trigonometric function which can be defined in terms of the ratio: (side
opposite)/(side adjacent)
Tangent
75.
Identify the trigonometric function which can be defined in terms of the ratio: (side
adjacent)/(side opposite)
Cotangent
76.
State the Pythagorean Theorem for a right triangle with sides a and b and hypotenuse c.
Ans a2 + b2 = c2
Basic play for Clever Catch® is simple. Two or more players toss the ball to each other,
answering the problem underneath or closest to their left thumb. Each problem is numbered and enclosed in its own space, assuring the child will know which problem to answer.
Answers are provided in this insert for independent play by students.
77.
What is the value of tan a ?
3/4
PLAYOFFS:
78.
What is the value of sin a ?
3/5
79.
What is the value of cos b?
3/5
3
150˚
/2
Cosine
What is the value of csc b?
81.
Use the law of cosines to find an expression equivalent to a2.
b2 + c2 - 2bc cos A
82.
Use the law of cosines to find an expression equivalent to b2.
a2 + c2 - 2ac cos B
83.
Identify a formula which uses angle C to find the area of triangle ABC.
1/2 ab sin C
84.
Identify a formula which uses angle A to find the area of triangle ABC.
1/2 bc sin A
a/sin A = b/sin B
85.
State the law of sines involving sides a and b.
86.
State the law of sines involving sides b and c.
b/sin B = c/sin C
87.
If sin x = .6 and cos x = .8, what is the value of sin 2x?
.96
88.
If sin x = .6 and cos x = .8, what is the value of cos 2x?
.28
89.
Name the quadrant of angle x if sin x > 0 and cos x < 0.
II
BEAT THE CLOCK:
The entire class plays cooperatively as one team, trying to better its own time and number
of correct answers in each game.
Directions:
1 Choose a timekeeper. You also will need a monitor - teacher or student - to keep track of correct answers.
90.
Name the quadrant of angle x if tan x > 0 and sin x < 0.
III
91.
Name the quadrant of angle x if sec x < 0 and csc x < 0.
III
92.
Name the quadrant of angle x if cot x < 0 and sin x < 0.
IV
93.
What is the value of sin 0?
0
94.
What is the value of sec-1(-1)?
π radians or 180˚
95.
What is the value of sin (sin-1.5) ?
.5
-1
The Trigonometry Clever Catch® provides an excellent way for children to practice algebra.
There are 100 color coded questions included (Blue = Radians, degrees, the unit circle,
and formulas; Orange = Trig identities and functions; Green = Solving trig functions and
translations). Clever Catch® can be used at school in organized classroom activities. It can
also be used at home. Grades 8+, Ages 13+.
Pairs of children toss the ball back and forth for one minute answering problems.
A scorekeeper tallies which team has the most correct answers in the time limit.
5/4
80.
TRIGONOMETRY
2 Divide the class into two lines of equal length, students facing each other.
3 At the timekeeper’s signal, toss Clever Catch® to the first student. As quickly as possible, this student reads and answers the problem underneath his/her left thumb.
96.
What is the value of sec-1(sec π/5)?
π/5
97.
Identify the expansion formula for sin (x + y).
sin (x + y) = sin x cos y + cos x sin y
98.
Identify the expansion formula for cos(x + y).
cos(x + y) = cos x cos y - sin x sin y
99.
What is the value of sin x if cos x = b for 0˚ < x < 90˚?
100.
What is the value of cos x if sin x = a for 90˚ < x < 180˚?
4 This student then tosses Clever Catch® to the student directly across from him/her in the second line. This student reads and answers the problem under his/her left thumb.
5 Play continues until all students in both lines have had a turn. When the last student has answered, the time and correct number of answers are recorded.
1 - b2
-
1 - a2
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SR-1568
QUESTION
ANSWER
1.
sin π/2 = 1
True
2.
tan 215˚> tan 75˚.
False
3.
cos 35˚ = sin 55˚
True
4.
tan x ≤ 1
False
5.
sin (x + y) = sin x + sin y
False
True
6.
tan2x + 1 = sec2x
7.
cos π/6 = 1/2
False
8.
tan 7π/3 = tan π/3
True
9.
If sin x = 4/5 in the first quadrant, then cos x = 3/5
True
10.
The period of the function f(x) = 2 sin 3x is π/3
False
11.
The amplitude of the function f(x) = -2 cos 4x + 3 is -2
?
For each real number x and each integer n, sin x = sin(x + 2nπ)
True
12.
False
13.
If y = sin (x - π/3), then π/3 is the phase shift
True
14.
tan x = sin x/cos x
True
15.
π radians is equivalent to 360 degrees
False
16.
The terminal side of a 230˚ angle in standard position is in the third quadrant.
True
17.
An angle whose terminal ray lies on one of the coordinate axes is called an obtuse
angle.
False
18.
| sin x - sin y | ≤ | x - y |
True
19.
If sin x = 3/5 for 90˚ < x < 180˚, then cos x = 4/5
False
20.
sin 2x = 2 sin x
False
21.
Which one of the following relationships is not true?
A. sin(-x) = - sin x
B. cos(-x)= - cos x C. tan(-x) = - tan x
B
22.
Which expression has the greatest value?
A. cos 30˚
B. cos 45˚
C. cos 60˚
A
23.
Which one of the following relationships is true?
A. cos 2x = 2cos x
B. cos 2x = 2cos x sin x
C. cos 2x = cos2x - sin2x
C
24.
Which one of the following relationships is not true?
A. sin(π - x) = sin x
B. cos(π - x) = - cos x
C. tan(π - x) = tan x
C
If 270˚ < x < 360˚ and sin x = - 4/5, then
A. cos x = 3/5
B. cos x = -1/5
C. cos x = 1/5
A
26.
If 180˚ < x < 270˚ and cos x = -.5, then
A. sin x = .5
B. sin x = 3 /2
C. sin x =3 /2
C
27.
If tan x = 2, how many solutions are there for x?
A. infinite
B. 2
C. 1
A
Which one of the following relationships is true?
A. csc x = 1/sec x
B. csc x = 1/sin x
C. csc x = 1/cos x
B
What is the period of y = tan x?
A. 2π
B. π
C. π/2
B
What is the maximum value of f(x) = 3 - sin [2(x - π)]?
A. 3
B. 2
C. 4
C
Which one of the following relationships is true?
A. tan x = 1 - cot x
B. tan x = sin x/cos x
C. tan x = 1 - cot 2 x
B
25.
28.
29.
30.
31.
QUESTION
32.
Name the quadrant of E θ if sin θ < 0 and cos θ > 0.
A. II B. III
C. IV
ANSWER
C
33.
Which one of the following relationships is not true?
A. cot2x + csc2x = 1
B. sin2x + cos2x = 1
C. 1 + tan2x = sec2x
A
34.
What is the phase shift for the function y = 2cos (2x - π/3)?
A. π/3
B. - π/3
C. π/6
C
35.
Which one of the following relationships is not true?
A. cos(cos-1.3) = .3
B. sin-1(sin 2π/3) = 2π/3
C. cos-1(cos 2π/3) = 2π/3
B
36.
Which one of the following functions is even?
A. y = cos x
B. y = sin x
C. y = tan x
A
37.
Which of the following functions is symmetric with respect to the y-axis?
A. y = cos x
B. y = sin x
C. y = tan x
A
38.
Which one of the following relationships is false?
A. sin2x + cos2x = 1
B. cos x = -sin x
C. sin 2x = 2sin x cos x
B
39.
What is the arc length on a circle of radius 3 which subtends a central angle of 60˚?
A. π
B. 180
C. 3
A
40.
Which of the following points is not on a unit circle centered at (0, 0)?
A. (1, 0)
B. ( 2 /2, 2 /2 )
C. (.5, .5)
C
41.
What is lim sin x?
0
42.
What is lim cos x?
1
43.
If (1/2, y) lies on a unit circle centered at (0, 0), what is a value of y?
44.
If (x, 3/5) lies on a unit circle centered at (0, 0), what is a value of x?
45.
What is the value of cos π?
46.
What is the value of sin π/3?
3 /2
47.
What is the value of tan 60˚?
3
48.
What is the value of sec (-45˚)?
49.
What is the value of sin 3π?
50.
What is the value of 2sin (π/6) cos (π/6)?
51.
Identify the amplitude of: y = 5 - 4sin [2(x + π/2)]
4
52.
Identify the period of: y = 5 - 4sin [2(x + π/2)]
π
53.
Identify the phase shift of: y = 5 - 4sin [2(x + π/2)].
-π/2
54.
Identify the maximum value of: y = 5 - 4sin [2(x + π/2)]
9
55.
Identify the minimum value of: y = 5 - 4sin [2(x + π/2)]
1
56.
Identify the value of x for 0 ≤ x ≤ 90˚ where tan x = cot x.
45˚
57.
Identify the reference angle of a 135˚ angle drawn in standard position.
45˚
3 /2 or 4/5 or -4/5
-1
2
0
3 /2
58.
Identify the reference angle of a 210˚ angle drawn in standard position.
30˚
59.
Identify the reference angle of a 2π/3 radian angle drawn in standard position. π/3 radian
60.
Identify the reference angle of a 7π/6 radian angle drawn in standard position.
π/6 radian
61.
What is the length of the shortest side in a 30˚-60˚ right triangle with a hypotenuse
length of 2?
1
3 /2