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