Periodic Functions
Sine, Cosine, Tangent
Unit Circle
Random Things
Jacks Trivia
100
Let a function have a period of 5 with the following values:
x: -2, 3, 4, 6, 12
f(x): 8, 10, 13, 21, 32
Find the value of f(27):
f(12 + 5*3) = f(12) = 32
100
Let Theta be an angle in standard position whose terminal ray intersects a circle centered at the origin at Point P. If Theta is equal to 5pi/3, which quadrant is Point P in?
Quadrant 4 (IV)
100
What is the value of sin(pi/2)?
sqrt(2)/2
100
What is ratio used for tangent (with x,y values)?
sin(x)/cos(x) or y/x
100
How old is Mr. Jacks?
25
200
What is the period of this function?
The period is 8.
200
Let Theta be an angle in standard position on a circle with radius of 1. If theta is equal to 7/8 of a circle, in the clockwise direction, what is the radian measure of theta?
-7pi/4
200
What is cos(3pi/2)?
0
200
What is the sum of the sine and cosine functions at pi/4?
sqrt(2)/2 + sqrt(2)/2 = sqrt(2)
200
How many years has Mr. Jacks been teaching?
This is year 3!
300
Find the value of f(-22)
f(-22) = f(2 + 8(-3)) = f(2) = 4
300
Let Theta be an angle in standard position on a circle with radius of 2. If theta is equal to 3/4 of a circle, in the counterclockwise direction, what is the radian measure of theta?
3pi/2
300
What is the value of cos(13pi/6)? Hint: You have to go beyond one full revolution of the unit circle.
sqrt(3)/2
300
Which radian(s) measure has a y value of 1/2?
pi/6 and 5pi/6
300
What College did Mr. Jacks go to?
UK
400
What is the period of a sin or cosine function? Hint: think of how long it takes for both the x,y values to repeat on the unit circle.
The period if 2pi
400
Let Theta intersect a point at (3, 10) on a circle of radius 13. Find the value of cos(theta).
cos(theta) = 3/13
400
What is the value of tan(pi/6)?
1/sqrt(3) or sqrt(3)/3
400
What group of ancient people founded the unit circle?
The ancient Greeks (Hipparchus)
400
What High School did Mr. Jacks go to?
Tates Creek High School
500
Using the unit circle, what is the value of sin(13pi/4)?
-sqrt(2)/2
500
Which quadrant would theta = -13pi/3 be in?
Quadrant 4 (IV)
500
What is the value of sin^2(pi/6) + cos^2(pi/3)?
1/2
500
What radian value between 0 and pi is tangent undefined?
At pi/2 (sin(pi/2)/cos(pi/2)) = 1/0 and you can not divide by 0.
500
What is the name of either one of Mr. Jacks' cats?
Boots and Peppa