trigonometry
trigonometry
Secondary Trigonometric Functions
MHF4U: Advanced Functions
The three secondary (reciprocal) trigonometric functions are:
• f (x) = csc x
• f (x) = sec x
• f (x) = cot x
Secondary Trigonometric Functions
Like the primary trigonometric functions, graphs of the
secondary trigonometric functions can be sketched by using
the 5 key points at 0, π2 , π, 3π
2 and 2π.
J. Garvin
If transformations are required, these points can be adjusted.
J. Garvin — Secondary Trigonometric Functions
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trigonometry
trigonometry
Secondary Trigonometric Functions
Secondary Trigonometric Functions
Example
Compare the graph of f (x) = csc x to g (x) = sin x.
Sketch a graph of f (x) = csc x.
J. Garvin — Secondary Trigonometric Functions
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J. Garvin — Secondary Trigonometric Functions
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trigonometry
trigonometry
Secondary Trigonometric Functions
Secondary Trigonometric Functions
Example
Compare the graph of f (x) = sec x to g (x) = cos x.
Sketch a graph of f (x) = sec x.
J. Garvin — Secondary Trigonometric Functions
Slide 5/11
J. Garvin — Secondary Trigonometric Functions
Slide 6/11
trigonometry
trigonometry
Secondary Trigonometric Functions
Secondary Trigonometric Functions
Example
Compare the graph of f (x) = cot x to g (x) = tan x.
Sketch a graph of f (x) = cot x.
J. Garvin — Secondary Trigonometric Functions
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J. Garvin — Secondary Trigonometric Functions
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trigonometry
trigonometry
Secondary Trigonometric Functions
Secondary Trigonometric Functions
Example
Example
Sketch a graph of f (x) = sec 2x.
Sketch a graph of f (x) = csc x − 2.
J. Garvin — Secondary Trigonometric Functions
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J. Garvin — Secondary Trigonometric Functions
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trigonometry
Questions?
J. Garvin — Secondary Trigonometric Functions
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