Graph-Based Reciprocal Reasoning

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| Questions: 20 | Updated: Oct 14, 2025
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1) The cosecant graph has vertical asymptotes whenever...

Explanation

Cosecant blows up where sine hits zero.

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About This Quiz
Graph-based Reciprocal Reasoning - Quiz

Do you know what happens to trig graphs when you flip them into their reciprocals? In this quiz, you’ll explore graphs of secant, cosecant, and cotangent, identifying their asymptotes, shapes, and relationships to sine, cosine, and tangent. Try this quiz to strengthen your graph interpretation skills with reciprocal functions.

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2) The secant graph has vertical asymptotes whenever...

Explanation

Secant blows up where cosine hits zero.

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3) The cotangent graph has vertical asymptotes whenever...

Explanation

Cotangent is undefined where sine hits zero.

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4) Which pair of graphs are reciprocals of each other?

Explanation

Cosine pairs with its reciprocal secant.

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5) Which pair of graphs are reciprocals of each other?

Explanation

Sine pairs with its reciprocal cosecant.

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6) In the graph of secant, the minimum points of cosine correspond to...

Explanation

Where cosine is at a minimum, secant is at a maximum.

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7) In the graph of cosecant, the maximum points of sine correspond to...

Explanation

Where sine is at a maximum, cosecant is at a maximum.

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8) In the graph of cotangent, vertical asymptotes occur at multiples of...

Explanation

Cotangent’s asymptotes line up with multiples of π.

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9) The graph of secant is undefined wherever...

Explanation

Secant is undefined where cosine is zero.

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10) The graph of cosecant is undefined wherever...

Explanation

Cosecant is undefined where sine is zero.

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11) The graph of cotangent is undefined wherever...

Explanation

Cotangent is undefined where sine is zero.

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12) If a graph has "u-shaped" branches opening up and down with asymptotes where cosine = 0, the graph must be...

Explanation

The “U-shaped branches” flanking cosine’s zeros are secant.

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13) If a graph has alternating "cup" and "cap" shapes with asymptotes where sine = 0, the graph must be...

Explanation

The alternating “cup/cap” shapes around sine’s zeros are cosecant.

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14) The reciprocal of a tangent graph is...

Explanation

The reciprocal of a tangent graph is cotangent.

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15) The reciprocal of a sine graph is...

Explanation

The reciprocal of a sine graph is cosecant.

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16) The reciprocal of a cosine graph is...

Explanation

The reciprocal of a cosine graph is secant.

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17) Which reciprocal graph has asymptotes at every multiple of π radians?

Explanation

Among the reciprocal graphs, the one with asymptotes at every multiple of π is cosecant.

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18) Which reciprocal graph has asymptotes at every multiple of π/2 radians?

Explanation

The reciprocal graph with asymptotes at every multiple of π/2 is secant.

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19) If the sine graph crosses zero at 0, π, and 2π, the cosecant graph at those same points will...

Explanation

Where sine crosses zero (0, π, 2π), cosecant has vertical asymptotes.

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20) If the cosine graph has zeros at π/2 and 3π/2, then the secant graph at those points will...

Explanation

Where cosine is zero (π/2, 3π/2), secant has vertical asymptotes.

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The cosecant graph has vertical asymptotes whenever...
The secant graph has vertical asymptotes whenever...
The cotangent graph has vertical asymptotes whenever...
Which pair of graphs are reciprocals of each other?
Which pair of graphs are reciprocals of each other?
In the graph of secant, the minimum points of cosine correspond to...
In the graph of cosecant, the maximum points of sine correspond to...
In the graph of cotangent, vertical asymptotes occur at multiples...
The graph of secant is undefined wherever...
The graph of cosecant is undefined wherever...
The graph of cotangent is undefined wherever...
If a graph has "u-shaped" branches opening up and down with...
If a graph has alternating "cup" and "cap" shapes...
The reciprocal of a tangent graph is...
The reciprocal of a sine graph is...
The reciprocal of a cosine graph is...
Which reciprocal graph has asymptotes at every multiple of π...
Which reciprocal graph has asymptotes at every multiple of π/2...
If the sine graph crosses zero at 0, π, and 2π, the cosecant...
If the cosine graph has zeros at π/2 and 3π/2, then the secant...
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