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1.5 ~ Graphs of Sine and Cosine Functions
In this lesson you will:
•Sketch the graphs of basic sine and cosine functions.
•Use amplitude and period to help sketch graphs.
•Sketch translations of these functions.
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1.5 ~ Graphs of Sine and Cosine Functions, Exercises of Trigonometry
In this lesson you will: • Sketch the graphs of basic sine and cosine functions. Use amplitude and period to help sketch graphs. Sketch translations of these ...
Typology: Exercises
2021/2022
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1.5 ~ Graphs of Sine and Cosine Functions
In this lesson you will:
- Sketch the graphs of basic sine and cosine functions.
- Use amplitude and period to help sketch graphs.
- Sketch translations of these functions.
(cos x, sin x )
f(x) = sin x
http://tube.geogebra.org/student/m45354?mobile=true
(cos x, sin x )
f(x) = cos x
http://tube.geogebra.org/student/m45354?mobile=true
Graph of f(x) = cos x
Domain: Range:
Period: Symmetry:
Domain: Range:
Period: Symmetry:
Let's look at it one part at a time: Amplitude: |a| Example 1 : Graph each of these.
y = a sin x
y = 3 sin x y = - 2 cos x
y = a sin(bx+c)+d
What effect do a, b, c and d have on the graph of trigonometric functions?
y = sin( 2 x) y^ =^ cos(^ x)
y = sin(bx)
Example 2 : Graph each of these. Period = 1 2
y = sin( 2 x - π) y^ =^ cos((^ )^ x^ +^ )
y = sin(bx - c)
Period = Horizontal shift = Example 4 : Graph each of these. π 2
y = sin( 2 x - π) y^ =^ cos((^ )^ x^ +^ )
y = sin(bx - c)
Period = Horizontal shift = Example 4 : Graph each of these. π 2
So, when we graph a sine or cosine function there are these things to consider: (^) Amplitude Period Phase shift (horizontal) Vertical shift y = 3 cos(2x - π) + 1 (^) Amplitude Period Phase shift (horizontal) Vertical shift Example 6: Sketch this function.
Example 7: Look at each of these graphs and write an equation in the form of y = a sin(b(x-h))+k or y = a cos(b(x-h)) + k x- axis tic marks =^ ,^ y- axis tic marks =^ 1 π 2