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JeopardyTrigonometry Review
PreCalculus Review Vocabulary Unit Circle Misc. Graphing
Trig. Functions
Solving Trig.
Equations
$100 $100 $100 $100 $100
$200 $200 $200 $200 $200
$300 $300 $300 $300 $300
$400 $400 $400 $400 $400
$500 $500 $500 $500 $500
Vocabulary for $100 Identify the supplement of the angle (if
possible).
3π4
Answer for Vocabulary $100
sup plement3π4
⎛⎝⎜
⎞⎠⎟=π4
Vocabulary for $200 Identify the co-terminal angle (if possible).
coterminal∠5π3
⎛⎝⎜
⎞⎠⎟=
Answer for Vocabulary $200
coterminal∠5π3
⎛⎝⎜
⎞⎠⎟=−
π3
Vocabulary for $300 Identify the reference angle of:
reference∠4π3
⎛⎝⎜
⎞⎠⎟=
Answer for Vocabulary $300
reference∠4π3
⎛⎝⎜
⎞⎠⎟=π3
Vocabulary for $400 Identify which function has the largest period.
A)y=4sinπ3
x−4⎛⎝⎜
⎞⎠⎟
B)y=3cos −2π5
x+π2
⎛⎝⎜
⎞⎠⎟
Answer for Vocabulary $400
A)y=4sinπ3
x−4⎛⎝⎜
⎞⎠⎟→ p=
2ππ3
=6
B)y=−3cos −2π5
x+π2
⎛⎝⎜
⎞⎠⎟→ p=
2π
−2π5
=−5
Vocabulary for $500 If a plane that is cruising at an altitude of
30,000 feet wants to land at Denver International Airport, it must begin its descent so that the angle of depression to the airport is 7°. How many miles from the airport must the plane begin descending?
Answer for Vocabulary $500
If a plane that is cruising at an altitude of 30,000 feet wants to land at Denver International Airport, it must begin its descent so that the angle of depression to the airport is 7°. How many feet from the airport must the plane begin descending?
30,000
7°
83°
7°X
tan 7°( ) =30,000
x
x=30,000tan 7°( )
=244,330
Unit Circle for $100 Find the value of .
€
cos(π )
Answers for Unit Circle $100cos π( ) =−1
Unit Circle for $200 Find the .
€
sin −π
2
⎛
⎝ ⎜
⎞
⎠ ⎟
Answers for Unit Circle $200
sin −π2
⎛⎝⎜
⎞⎠⎟=−1
Unit Circle for $300 Determine the value:
cos7π6
⎛⎝⎜
⎞⎠⎟+sin
5π3
⎛⎝⎜
⎞⎠⎟
Answers for Unit Circle $300
cos7π6
⎛⎝⎜
⎞⎠⎟+sin
5π3
⎛⎝⎜
⎞⎠⎟=−
32
−32
=−232
=− 3
Unit Circle for $400 Simplify the expression:
tan2π3
⎛⎝⎜
⎞⎠⎟
cos5π3
⎛⎝⎜
⎞⎠⎟
Answers for Unit Circle $400
tan2π3
⎛⎝⎜
⎞⎠⎟
cos5π3
⎛⎝⎜
⎞⎠⎟
=− 312
=−2 31
=−2 3
Unit Circle for $500 Evaluate all six trig functions when
ϑ =11π
6
Answers for Unit Circle $500
sin11π6
⎛⎝⎜
⎞⎠⎟=
32
cos11π6
⎛⎝⎜
⎞⎠⎟=−
12
tan11π6
⎛⎝⎜
⎞⎠⎟=−
13=−
33
csc11π6
⎛⎝⎜
⎞⎠⎟=
23=2 33
sec11π6
⎛⎝⎜
⎞⎠⎟=−2
cot11π6
⎛⎝⎜
⎞⎠⎟=− 3
Misc for $100 Find the inverse angle of the function.
sec−1 −1( )
Answers for Misc for $100
sec−1 −1( )=π
Misc for $200 Find the inverse angle of
sec−1 2 33
⎛
⎝⎜⎞
⎠⎟
Answers for Misc for $200
sec−1 2 33
⎛
⎝⎜⎞
⎠⎟=sec−1 2
3⎛⎝⎜
⎞⎠⎟→
ϑ =π6
or11π6
Misc for $300 The point (5, -3) is on the terminal side of the
angle. Find the exact value for the sine and tangent function.
Answers for Misc for $300
(5,−3)→ x=5,y=−3
r = 52 + −3( )2 = 34
sinϑ =yr=−
334
=−3 3434
tanϑ =yx=−
35
Misc for $400 Given the information below, find the exact
value of the sine and cosine of the function.
sec(ϑ )=−53
tan ϑ( ) > 0
Answers for Misc for $400
If sec(ϑ )=−53
& tan ϑ( ) > 0
then sec(ϑ ) =−53
=rx→ x=−3,r =5
r→ −3( )2 + y2 =5
9 + y2 =25→ y= 16 but tan ϑ( ) > 0→ y=−4
thus sinϑ =yr=−45,cosϑ =
−35
Misc for $500 Simplify the expression into using only one
trig function.
tanϑcotϑ
•secϑcscϑ
Answers for Misc for $500
tanϑcotϑ
•secϑcscϑ
=
sinϑcosϑcosϑsinϑ
•
1cosϑ1
sinϑ
=
sin2ϑcos2ϑ
•sinϑcosϑ
=tan3ϑ
Graphing Trig Functions for $100Which trig function has the largest amplitude?A) f (x)=−4sin 2x+1( )B) g(x) =2sin(2x)
Answers for Graphing Trig Functions for $100
AA) f (x)=−4sin 2x+1( )B) g(x) =2sin(2x)
Graphing Trig Functions for $200
Given the function provided below identify the amplitude, period, and midline.
y=−5cos2π3
x−4( )⎡⎣⎢
⎤⎦⎥−5
Answers for Graphing Trig Functions for $200
y=−5cos2π3
x−4( )⎡⎣⎢
⎤⎦⎥−5
a =5midline:y=−5
period=2π2π3
=3
Graphing Trig Functions for $300
Given the function provided below and the point (5,7). Find the value of c.
y=−3sin2π5
x+c⎛⎝⎜
⎞⎠⎟+ 4
Answers for Graphing Trig Functions for
$300y=−3sin
2π5
x+c⎛⎝⎜
⎞⎠⎟+ 4 & 5,7( )
7 =−3sin2π5
5 +c⎛⎝⎜
⎞⎠⎟+ 4
−1=sin2π5
5 +c⎛⎝⎜
⎞⎠⎟→ −1=sin 2π +c( )
3π2
=2π +c→3π2
=4π2
+c
c=−π2
Graphing Trig Functions for $400
Jacob and Emily ride a Ferris wheel at a carnival in Billings, Montana. The wheel has a 16 meter diameter, and turns at three revolutions per six minutes, with its lowest point one meter above the ground. Assume that Jacob and Emily's height h above the ground is a sinusoidal function of time t, where t =0 represents the lowest point on the wheel and t is measured in seconds. Write the equation for h in terms of t for a cosine sinusoidal function.
Answers for Graphing Trig Functions for
$400period =
2πb
=2min→ b=π
y=8cos πx+c( )+ 9& (0,1)
1=8cos π (0)+c( )+ 9−1=cos(c)
c=π → y=8cos πx( )+ 9
Graphing Trig Functions for $500
Graph the function and label all identify all parts (amplitude, period, midline, and x-intercept)
y=4cos −4π5
x−π⎛⎝⎜
⎞⎠⎟
Answers for Graphing Trig Functions for
$500y=4cos −
4π5
x−π⎛⎝⎜
⎞⎠⎟
X-values Y-values
-5/2 =-25/8 0
-30/8 4
-35/8 0
-40/8 -4
-45/8 0
period =2π
−4π5
=−52
section=period
4=−
58
Solving Trig Equations for $100
Solving the equation for x:
2sin x−1=0
Answers for Solving Trig Equations for $100
2sin x−1=0
sinx=12
x=π6,5π6
Solving Trig Equations for $200
Solve the equation for x:
2sin2 x−sinx=1
Answers for Solving Trig Equations for $200
2sin2 x−sinx=1
2sin2 x−sinx−1=0
2sinx+1( ) sinx−1( )=0
sinx=−12,sinx=1
x=7π6,11π6
,π2
Solving Trig Equations for $300
Solve the equation for x:
sin x + 2 =−sinx
Answers for Solving Trig Equations for $300
sin x + 2 =−sinx
2sinx=− 2
sinx=−22
x=5π4,7π4
Solving Trig Equations for $400
Solve the equation for x:
2cos 3x−1( )=0
Answers for Solving Trig Equations for $400
2cos 3x−1( )=0
cos 3x−1( )=0π2=3x−1 &
3π2
=3x−1
x=
π2+1
3=π +26
& x=
3π2
+22
3=3π +26
Solving Trig Equations for $500
Solve the equation for x:
3tanx
2⎛⎝⎜
⎞⎠⎟+ 3=0
Answers for Solving Trig Equations for $500
3tanx
2⎛⎝⎜
⎞⎠⎟+ 3=0
tanx2
⎛⎝⎜
⎞⎠⎟=−1
3π4
=x2&
7π4
=x2
x=6π4
=3π2
& x=14π4
=7π2
