Questions and Answers
What is the amplitude of the Cosine function?
What is the period of the Tangent function?
pi
What is the range of the Cosecant function?
What is the range of the Secant function?
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What is the domain of the Cotangent function?
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What is the domain of the Inverse Sine function?
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What x intercept does the Inverse Cosine function have?
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What is the period of the Inverse Tangent function?
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What is the vertical asymptote of the Inverse Cosecant function?
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What is the range of the Inverse Secant function?
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What is the y intercept of the Inverse Cotangent function?
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Study Notes
Cosine
- Parent function with amplitude of 1.
- Period of 2π and no phase or vertical shift.
- X intercepts at odd multiples of π/2.
- Y intercept at (0, 1), with a range of [-1, 1].
- Domain includes all real numbers; maximum value is 1, minimum is -1.
Tangent
- Parent function with an amplitude of 1 and period of π.
- No phase or vertical shift present.
- Range covers all real numbers, while domain is restricted to [-π/2, π/2].
- Neither maximum nor minimum value exists.
Cosecant
- Reciprocal of the cosine function, amplitude of 1.
- Period of 2π, phase shift of 0, vertical shift of 0.
- Range of (-∞, -1] ∪ [1, ∞) with X asymptotes at multiples of π.
- Domain varies based on asymptotes, with no defined maximum or minimum.
Secant
- Also the reciprocal of the cosine function, with similar attributes to cosecant.
- Amplitude of 1 and period of 2π; no phase or vertical shift.
- Range of (-∞, -1] ∪ [1, ∞) and X asymptotes located at odd multiples of π/2.
- Domain influenced by asymptotes; no defined maximum or minimum.
Cotangent
- Parent function similar to tangent, with amplitude of 1.
- Period of π and absence of phase or vertical shift.
- Range includes all real numbers, while domain is limited to [0, π].
- No maximum or minimum values present.
Inverse Sine
- Domain confined to [-1, 1] with a range of all real numbers.
- Vertical asymptotes at [-1, 1].
- Period extends to 2π; X and Y intercepts at (0, 0).
- Used primarily for determining angles; lacks defined maximum or minimum.
Inverse Cosine
- Domain limited to [-1, 1], encompassing the same range as inverse sine.
- Vertical asymptotes also at [-1, 1].
- Period of 2π; X intercept at (1, 0) and Y intercept at (0, π/2).
- Utilized for angle determination; no maximum or minimum defined.
Inverse Tangent
- Domain encompasses all real numbers with range of [-π/2, π/2].
- Period extends to 2π; X and Y intercepts at (0, 0).
- Vertical asymptotes at -π/2 and π/2, used for angle calculation.
Inverse Cosecant
- Domain consists of all real numbers with a range of [0, π].
- No X intercepts are present, and Y intercept occurs at (0, π/2).
- Vertical asymptotes located at 0 and π; assists in angle finding.
Inverse Secant
- Domain defined as (-∞, -1] ∪ [1, ∞); range includes [0, π/2) ∪ (π/2, π].
- Horizontal asymptote at y = π/2; X intercepts at (1, 0) with no Y intercept.
Inverse Cotangent
- Domain is (-∞, -1] ∪ [1, ∞); range specified as (0, π).
- Horizontal asymptotes located at x = 0 and x = π.
- No X intercepts, with Y intercept at (0, π/2).
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