Podcast
Questions and Answers
What is the period of the cosine function?
What is the period of the cosine function?
- 3Ï€
- 2Ï€ (correct)
- π
- 5Ï€
For what values of x does tanx increase indefinitely?
For what values of x does tanx increase indefinitely?
- From 0 to π (correct)
- From π to 2π
- From 0 to 3Ï€
- From 0 to 2Ï€
Which trigonometric function's graph increases from 0 to 1 as x increases?
Which trigonometric function's graph increases from 0 to 1 as x increases?
- cosx
- cotx
- tanx
- sinx (correct)
In the given table, what is the value of y when x = π?
In the given table, what is the value of y when x = π?
What does the graph of y = cosx do periodically according to the text?
What does the graph of y = cosx do periodically according to the text?
What happens to tanx as x approaches 2Ï€ starting from 0?
What happens to tanx as x approaches 2Ï€ starting from 0?
What is the period of the cosine function?
What is the period of the cosine function?
In which interval does the graph of y = sinx fall within?
In which interval does the graph of y = sinx fall within?
If x represents a variable angle, what are the values of sin(Ï€/3) and cos(Ï€/6)?
If x represents a variable angle, what are the values of sin(Ï€/3) and cos(Ï€/6)?
Which trigonometric function has a period of π?
Which trigonometric function has a period of π?
What is the value of cos(45°)?
What is the value of cos(45°)?
If the graph of y = sinx is shifted 2Ï€ units to the right, what does the curve do?
If the graph of y = sinx is shifted 2Ï€ units to the right, what does the curve do?
For the angle θ = 45°, what is the value of sin(2θ)?
For the angle θ = 45°, what is the value of sin(2θ)?
What is the value of cosθ if sinθ = $\frac{1}{2}$?
What is the value of cosθ if sinθ = $\frac{1}{2}$?
If secθ = -3, what is the value of cosθ?
If secθ = -3, what is the value of cosθ?
Calculate the value of tan(60°).
Calculate the value of tan(60°).
What is the value of cot(-45°)?
What is the value of cot(-45°)?
If sinθ = $-\frac{1}{2}$, find the value of cosecθ.
If sinθ = $-\frac{1}{2}$, find the value of cosecθ.
Flashcards
Period of cosine
Period of cosine
The horizontal distance required for a cosine graph to repeat its pattern
Tanx increase indefinitely
Tanx increase indefinitely
Tangent function increases without bound at specific x values in a range
sinx graph increase
sinx graph increase
Sine's graph increases from 0 to 1 as x moves from 0 to π/2
y=cos(x) periodicity
y=cos(x) periodicity
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tan(x) as x approaches 2Ï€
tan(x) as x approaches 2Ï€
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sinx graph interval
sinx graph interval
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sin(Ï€/3) and cos(Ï€/6)
sin(Ï€/3) and cos(Ï€/6)
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cos(45°)
cos(45°)
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Shifting sin(x)
Shifting sin(x)
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sin(2θ) for θ = 45°
sin(2θ) for θ = 45°
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cosθ given sinθ = 1/2
cosθ given sinθ = 1/2
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cosθ if secθ = -3
cosθ if secθ = -3
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tan(60°)
tan(60°)
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cot(-45°)
cot(-45°)
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cosecθ if sinθ = -1/2
cosecθ if sinθ = -1/2
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Study Notes
Graphs of Trigonometric Functions
- The period of the sine function is 2Ï€, meaning that the graph will repeat itself every 2Ï€ units.
- The graph of y = sinx increases and decreases periodically within one unit of the Y-axis.
- The graph of y = sinx can be shifted 2Ï€ to the left or right, and it will fall back on itself.
Graph of Cosine Function
- The period of the cosine function is 2Ï€, meaning that the graph will repeat itself every 2Ï€ units.
- The graph of y = cosx increases and decreases periodically within one unit of the Y-axis.
- The graph of y = cosx can be shifted 2Ï€ to the left or right, and it will fall back on itself.
Graph of Tangent Function
- The period of the tangent function is π, meaning that the graph will repeat itself every π units.
- The graph of y = tanx increases indefinitely as x approaches π/2.
- The graph of y = tanx does not exist for x = π/2.
Trigonometric Identities
- sin(–θ) = –sinθ
- cos(–θ) = cosθ
- tan(–θ) = –tanθ
Trigonometric Functions of Special Angles
- The trigonometric functions of 0°, 30°, 45°, 60°, and 90° are tabulated in a standard table.
- Co-terminal angles have the same values of trigonometric functions.
Solving Trigonometric Equations
- To solve trigonometric equations, use the identities and properties of trigonometric functions.
- Example: tanθ + tanθ = 2, find the value of tan²θ + tan²θ.
- Example: Find the value of cos765° using the periodic nature of the cosine function.
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