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Questions and Answers
What is the period of the cosine function?
For what values of x does tanx increase indefinitely?
Which trigonometric function's graph increases from 0 to 1 as x increases?
In the given table, what is the value of y when x = π?
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What does the graph of y = cosx do periodically according to the text?
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What happens to tanx as x approaches 2Ï€ starting from 0?
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What is the period of the cosine function?
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In which interval does the graph of y = sinx fall within?
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If x represents a variable angle, what are the values of sin(Ï€/3) and cos(Ï€/6)?
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Which trigonometric function has a period of π?
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What is the value of cos(45°)?
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If the graph of y = sinx is shifted 2Ï€ units to the right, what does the curve do?
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For the angle θ = 45°, what is the value of sin(2θ)?
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What is the value of cosθ if sinθ = $\frac{1}{2}$?
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If secθ = -3, what is the value of cosθ?
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Calculate the value of tan(60°).
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What is the value of cot(-45°)?
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If sinθ = $-\frac{1}{2}$, find the value of cosecθ.
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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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Description
Test your knowledge of trigonometry with this quiz based on a table of values for cosine and sine functions. Explore the relationship between angles, cosine, and sine using the given data points and transformations. Practice plotting graphs and understanding trigonometric identities.
