Definitions
Trig-Calculations
It's A Small World After All!
Ferris Wheel FUN!
(NOT)Pedro Pascal
100
This trigonometry ratio relates hypotenuse and adjacent
What is cosine?
100
We know that cos(136) = -0.71934. Give me three more angles where cos(theta) = -0.71934. They have to be between -360 to 360 degrees only.
What are 224 degrees, -136 degrees, -224 degrees?
100
The formula to find the sum of an arithmetic sequence is: (where n is the number of terms to be added in a sequence. Find the sum of the series defined by:
sum_(n = 1)^15 (-2n-7)
S_n = (a_1 + a_n)n/2
What is -345?
100
Given the equation: y = 50 + 30sin(20t), which is the equation of the height of a Ferris wheel rider (in feet) starting at 3:00 position and moving in a counterclockwise direction (where t is # of seconds), identify the different parts of this equation, such as its midline, radius/amplitude, period, and average speed.
What are: midline = 50 feet, radius = 30 feet, average speed is 20 degrees per second and period = 18 seconds ?
100
Using Pascal's Triangle only, expand (x - 5)3. Simplify all terms in your answer.
What is x3 -15x2 + 75x - 125?
200
We know that sin(60) = sin(120). This is because 60 degrees is what type of angle?
Is it "reference" angle?
200
We know that sin 26o = 0.43837. Give me three more angles where sin(theta) = 0.43837. They have to be between -360 to 360 degrees only.
What are 154 degrees, -334 degrees, -206 degrees?
200
Write this sum in sigma notation: -17 -14 - 11 - 8 - 5 - 2 + 1 + 4 + … + 34 . Do NOT find the value of the sum.
What is sum_(n = 1)^18 (-17 + 3(n - 1)) OR sum_(n = 1)^18 (-20 + 3n)
200
In this equation, f(t) represents the height of a platform on a Ferris wheel in feet after t seconds. f(t) = 80+20 sin(15t).
Find the time(s) between t = 0 and t = 24 when the platform reaches a height of
80 + 10(sqrt3)
feet off the ground. Use exact values ONLY. (How would you type your answers on the calculator?)
What are t = 4 seconds and t = 8 seconds?
200
Using Pascal's Triangle only, expand (2x - 3)4. Simplify all terms in your answer.
What is 16x4 - 96x3 + 216x2 - 216x + 81?
300
What do we call the distance from the center of the ferris wheel to the ground?
Is it midline?
300
Using trigonometry, and find the value for x (exact value only):
What is
x = 5(sqrt2)?
300
Explain and draw what h(15)-h(12)3 means on this graph below:
What is "The average velocity from x = 12 to x = 15" or the slope from x = 12 to x = 15?
300
The graph of the height of a rider on a Ferris Wheel is shown below. What is the rider's starting position and the direction they are moving (clockwise or counterclockwise?)
What is: The starting position is at 12:00 (or at 90 degrees) and it is moving in a clockwise direction ?
300
Using Pascal's triangle, find how many ways to arrange 5 objects out of a total of 8 objects where order does not matter.
What is 56 different ways to arrange?
400
The only triangles that will work when using trig functions are...?
What are right triangles?
400
Using trigonometry, find the exact values of a and c:
What are a = 3 and c = 3(sqrt2)?
400
Solve the exact value of x for the following exponential equation:
72x - 17 = 64x + 3
What is x = (3ln(6) + 17ln(7))/(2ln(7) - 4 ln(6)) OR
x = (3log7(6) + 17)/(2 - 4log7(6))?
400
Write two equations: One cosine and one shifted sine for the graph below.
What are: y = 5cos(10t) and y = 5sin(10(t + 9)) or y = 5sin(10t + 90) or y = 5sin(10t - 270)?
400
Johanna made 5,280 three-scoop ice cream cones for Jonathan's Senior graduation. How many three-scoop ice cream bowls can Jonathan make?
What is 880 three-scoop bowls?
500
What do you call the time (in seconds) it takes for the whole trig graph to complete one full cycle/rotation?
What is period?
500
Using trigonometry, calculate the exact value for a:
What is a = 4/(sqrt(3)) ?
500
A certain radioactive substance decays a quarter of itself every minute. Initially, there are 50 grams of this substance. How much substance will be left after 4 minutes? Give exact values ONLY. (Like how would you type this in the calculator?)
What is y = 50(1/4)4 OR y = 50(0.25)4?
500
Find two angles, between -360 to 360, with the same as the value of cos(32 degrees).
What are 328 degrees and -328 degrees?
500
Using Pascal's Triangle, expand (a + b)12. Simplify all terms.
What is a12 + 12a11b + 66a10b2 + 220a9b3 + 495a8b4 + 792a7b5 + 924a6b6 + 792a5b7 + 495a4b8 + 220a3b9 + 66a2b10 + 12ab11 + b12 ?