Graphs of Trigonometric Functions

Presentation

•

Mathematics

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10th - 12th Grade

•

Medium

•

CCSS

HSF-IF.C.7E, HSF.TF.A.4

Standards-aligned

Elo Cheng

Used 11+ times

FREE Resource

11 Slides • 10 Questions

Graphs of Trigonometric Functions

By Elo Cheng

Graph of the Sine Function

The sine function is a set of ordered pairs of real numbers. Each ordered pair can be represented as a point of the coordinate plane. The domain of the sine function is the set of real numbers, that is, every real number is a first element of one pair of the function.

Multiple Choice

What is the domain and range of y=sinx?

D: (-∞, ∞)
R: [-1, 1]

D: (-∞, ∞)
R: [-π, π]

D: (∞, -∞)
R: [-1, 1]

D: (-∞, ∞)
R: [-∞, ∞]

On this graph, we plot the points whose coordinates are given in the table. Through these points, we draw a smooth curve.

Each time we increase or decrease the value of x-coordinates by a multiple of 2π, the basic curve is repeated. Each portion of the graph in an interval of 2π is one cycle of the sine curve.

The graph of the function y=sinx is called a periodic function with a period of 2π.

Camparing the graph of the unit circle and the graph of y=sinx in the figures above.

Multiple Choice

The period of a function is

how long one cycle is before the function repeats

how high and low the function goes from the center line

the range of the function

Multiple Choice

What does a negative 'a' value cause?

A negative amplitude

A reflection across the y-axis

No effect

A reflection across x-axis

Multiple Choice

The __________ represents half the distance between the max and min of a sine or cosine graph.

Period

Frequency

Extreme Values

Amplitude

Multiple Choice

What is the amplitude of the graph?

Multiple Choice

The amplitude of a sine or cosine wave measures the distance from the midline to the "top" of the wave, which is also the distance from the midline to the "bottom" of the wave.

True

False

Multiple Choice

Calculate the period of the curve

$4\pi$

$2\pi$

Multiple Choice

Calculate the period of the curve

$4\pi$

$2\pi$

-1

Multiple Choice

What is the period of
y= -3 sin(x)

2π

3π

4π

Multiple Choice

In the equation

$f\left(\theta\right)=7\sin\left(\theta\right)+2$ , what are the minimum and maximum values of the function?

min = 5; max = 9

min = 2; max = 7

min = -5; max = 9

min = -9; max = -5

Graphs of Trigonometric Functions

By Elo Cheng

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