Mystery Cretaceous Breakout

Trigonometry

Mystery Cretaceous Breakout

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Trigonometry

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Intro

Enter at your own risk, you must solve all the problems to exit

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Mission 1

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The graph below is equivalent to which function?

y = -cosx

y = cosx

y = sinx

y = tanx

The graph below is equivalent to which function?

y = -cosx

y = cosx

y = sinx

y = tanx

csc^2(x)

sec^2(x)

cot^2(x)

sin(x)

-11csc^2(x)

-11sec^2(x)

-11sin^2(x)

-csc^2(x)

csc^2(x)

sec^2(x)

-(6^1/2)

-(6^1/2)

(-2)(6^(1/2))

64/289

161/289

128/289

64/289

132/289

Completed

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Mission 2

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Drag and discover

The function f(θ) = tan(θ) represents the value of y/x on the unit circle.The period is π in radians. When we multiply the angle θ by 3, the length of the period will become . The period of the function would then equal .

faster3π

shorterπ/3

longer3π

longerπ/3

longerπ/3

The function f(θ) = sin(θ) represents the value of a . on the unit circle. The period is b . in radians. When we multiply the angle θ by 1/4, the length of the period will become c . The period of the function would then equal d .

a.y valueb.2π c.longer d.π/4

a.x valueb.2π/4 c.shorter d.8π

a.y valueb.8π c.shorter d.8π

a.y valueb.2π c.longer d.8π

a.y valueb.π c.shorter d.8π

a.y valueb.2π c.longer d.π/8

longerπ/3

How would you go about finding the best way to get an angle θ coterminal to -2π/3 , where 0≤θ<2π.

Subtracting 2π from angle

multiplying 2π to the given angle

adding 2π/3 to get coterminal

to find coterminal, subtract 360 degrees

multiplying -2π to angle

adding 2π to angle

longerπ/3

Which scenario below is an example of a phase shift?

two radio waves starting at the same time

the highest point in a pendulum swing

a sound wave starts slightly before another

difference between midline and amplitude

difference between the midline from two waves

adding height to an amplitude

longerπ/3

The point lies in quadrant 4, what is the value of x in simplest form?

-π/3

1/3

1/6

π/3

The graph below is equivalent to which function?

y = 3sin(x/3)-2

y = 5cos(x/2)-1

y = 3sin(2π)-2

y = 3cos(x/3)-2

The graph below is equivalent to which function?

y = 2sin(x/3)+3

y = 2sin(x)+3

y = sin(2π)+3

y = 2cos(x)+3

Max=2100mL air

Max=2200mL air

Max=2120mL air

Max=2110mL air

Write a sine function that has an amplitude of 2, a midline of y = 4 and a period of 2/3

y = 2sin(3x)+4

y=2sin(3πx)+4

y = 4sin(2π)+2

y = 2sin(x)+4

What is the derivative of sinx?

-cosx

cscx

cosx

secx

What is the identity of 1-cos^2(x) equivalent to?

2sin^2(x)

sinx

sec^2(x)

sin^2(x)

What quadrant does (-cosx,-sinx) appear in?

quadrantIV

quadrant I

quadrant III

quadrant II

-1/2

1/2

2π

1/4

Mission 3

Completed

Completed

Locked

Eli takes a trip to an amusement park and rides a Ferris wheel. The Ferris wheel has a maximum height of 345 ft and a minimum height of 25 ft. His car first reaches the bottom of the Ferris wheel at a time t=0.75 minutes. The next time it reaches the bottom of the Ferris wheel occurs at a time of t=3.75 minutes. What is the period in this context?

2 min

3 min

.75 min

Wronganswer

1.5 min

4 min

The identity sin(2x) is equivalent to which of the following

adjacent/hypotenuse

sinxcosx

2sinxcosx

Based on the standard form |A|cos(Bx+C)+D,What is the value of B in the equation -2cos(3πx+8)-4

3π

-2

-4

3π

Calculate the phase shift for -2cos(3πx+8)-4

3π/8 units to the left

8/3π to the right

8 units to the left

8/3π units to the left

8π units to the left

3π

Calculate the period for 4sin(3πx+5)-2

3/2

2π/3

3π/2

3π

2/3

3π

What is amplitude?

Half the distance between the maximumand minimum values of the function

The distance from the maximum to the minimum values of the function

The distance from the midline to the x axis.

Remember the code

216

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Completed

Completed

Completed

Mission 4

Given the following point on the unit circle, find the angle, to the nearest tenth of a degree (if necessary), of the terminal side through that point, 0∘ ≤θ<360∘ .P = (3/5 , 4/5)

53.1

52.3

51.8

Find an angle coterminal to −π/6 , where 0≤θ<2π.

11π/6

5π/6

8π/6

60.43

59.41

60.42

59.8

8.2

7.9

8.1

7.8

57.9

58.2

57.1

58.3

57.3

58.3

Angle x is positive.Given: sinx=3/5Find: cos2x

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