trig functions and iroc/aroc by kethompson426 on emaze

Opening Slide

Trigonometric Functions & Limits

- 1.6 and 2.1 -

Link to Slide next

HUNTER, GRETCHEN, KATIE, SAM, DINAH, AND KRISSY

Trigonometric Functions (1.6)

The radian measure of the angle ACB at the center of the unit circle equals the length of the arc that ACB cuts from the unit circle

S = arc length

R= radius

Theta= arc angle in radians

All of these functions are periodic functions. A function f(x) is periodic if there is a positive number p such that f(x+p) = f(x) for every value of x.

trigonometric formulas

sinx= y/r

cosx= x/r

tanx= y/x

cscx= r/y

secx= r/x

cotx= x/y

Cosx and Secx are even functions because their graphs are symmetric about the y axis.

The other four trig functions are odd- their graphs are symmetric to the origin.

y= Asin[(2π/B)(x-C)] + D

a: the vertical stretch or shrink; reflection over x axis

b: horizontal stretch or shrink; reflection over y axis

c: horizontal shift

d: vertical shift

[A] is the amplitude, [B] is the period, C is the horizontal shift, and D is the vertical shift.

y= af(b(x+c)) + d

Remember

The period is equal to 2π/B

Cosx and Sinx have a period of 2π , domains from negative infinity

to positive infinity, and ranges from negative one to one.

Secx and Cscx also have a period of 2π. Tanx and Cotx have a period

of π.

Question - Leonardo DiCaprio

Justin and Justin were on a ferris wheel thats height varied sinusoidally with time. The highest point on the wheel was 43 feet above the ground, the wheel makes a full circle every 8 seconds, and has a diameter of 40 feet. What would the graph look like?

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A)

B)

C)

Video Countdown

Video - Dancing Pig

Correct!

continue

Link to Object #The End

Title - Type B

AROC & IROC

A moving body's average speed during an interval of time is found by dividing the distance covered by the elapsed time.

A moving body's instantaneous speed during a particular moment is found by using the limit of the difference quotient.

The AROC is synonymous with the slope of the secant line.

The IROC is synonymous with the slope of the tangent line.

A. 112ft/sec; 134 + 2h

Link to Object #Video - Hair Stand on End

D. 112ft/sec; 224 + 16h

Link to Object #Video - Hair Stand on End

C. 12ft/sec; 224 + 16h

Link to Object #Video - Hair Stand on End

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Question - Pac-Man

A guy jumps from a plane cruising at 1500 ft. The man's fall is defined by the equation y=16t^2. What is his AROC from his jump (o sec) to 7 sec? WHat is his IROC at 7 sec?

B. 36ft/sec; 264 + 6h

Link to Object #Video - Dancing Pig

Video - Cat Playing the Piano

Correct!

continue

D

Title - Type B

Limits & Sandwich Theorem

A limit is the value that a function or sequence "approaches" as the input or index approaches some value.

Sometimes you cannot find a limit directly; you can find a limit indirectly using the Sandwich Theorem. In this theorem, one function, f, is “sandwiched” between the values of two other functions, g and h. If the two functions, g and h, have the same limit as x approaches c, then f will have an identical limit.

If g(x)≤f(x)≤h(x) for all x≠c in some interval about c, and

lim x→c g(x)=lim x→c h(x) =L then:

limx→c f(x)= L

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Question - Breaking Bad

2

20

40

200

300

Alex joins a 100-mile sprint competition, and runs at a constant speed of 10m/s. Time is denoted as t and distance as F, we can construct F(t)=t⋅V .

What is limit of F as t is approaching 20?

Video - Charlie Chaplin

Correct!

continue

200

Dialogue

Works cited

Unit circle picture https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwj4isjA-onPAhXM7yYKHX8ED5IQjRwIBw&url=http%3A%2F%2Fmathonweb.com%2Fhelp_ebook%2Fhtml%2Ftrigonometry.htm&bvm=bv.132479545,d.eWE&psig=AFQjCNFS9fgKA-sRuwkAhwiSxCENuGPv5A&ust=1473774096461281 Trig graphs https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiFhp6B_YnPAhUEPCYKHSakCI8QjRwIBw&url=http%3A%2F%2Fwww.algebra-answer.com%2Ftutorials-2%2Fgreatest-common-factor%2Freview-of-trigonometric.html&bvm=bv.132479545,d.eWE&psig=AFQjCNFKJZv3tKRiT1f0vV-9cXqa1CgFKg&ust=1473774773193591 AROC https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjf4_e3tYzPAhWGYyYKHU3BB_EQjRwIBw&url=%2Furl%3Fsa%3Di%26rct%3Dj%26q%3D%26esrc%3Ds%26source%3Dimages%26cd%3D%26cad%3Drja%26uact%3D8%26ved%3D0ahUKEwjf4_e3tYzPAhWGYyYKHU3BB_EQjRwIBw%26url%3Dhttp%253A%252F%252Fwww.mesacc.edu%252F~marfv02121%252Freadings%252Faverage%252F%26psig%3DAFQjCNGKakSq-ftdsi1fNYm9TOtzHPdl7w%26ust%3D1473858621534000&psig=AFQjCNGKakSq-ftdsi1fNYm9TOtzHPdl7w&ust=1473858621534000 IROC https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwi8jeaJtozPAhUB7CYKHRL0B2UQjRwIBw&url=https%3A%2F%2Fmath.la.asu.edu%2F~arce%2Fmat210_web%2Flessons%2FCh1%2F1_5%2F1_5olb.htm&bvm=bv.132479545,d.eWE&psig=AFQjCNFxW7QfYQux5ApUQISIuN65Xh8qJA&ust=1473858781055680 Youtube? https://youtu.be/1Hoev0SIzjw Limits https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiK7Oq5vYzPAhVIeCYKHWJXB_sQjRwIBw&url=http%3A%2F%2Fwww.shelovesmath.com%2Fcalculus%2Fdifferential-calculus%2Fintroduction-to-limits%2F&psig=AFQjCNETDyEERLINyhjvthqo8iAgE136Tw&ust=1473860771890901

The End

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