Reciprocal & Inverse Trigonometric Functions (Edexcel A-Level Mathematics): Quizzes

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Reciprocal Trig Functions - Graphs
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What is the definition of the cosecant function?

cscθ=1sinθ\csc \theta = \frac{1}{\sin \theta}

At which values of θ\theta does cscθ\csc \theta have vertical asymptotes?

θ=0,180,360,\theta = 0^\circ, 180^\circ, 360^\circ, \dots

What is the range of the cosecant function?

(,1][1,)(-\infty, -1] \cup [1, \infty)

What is the period of the cscθ\csc \theta function?

360360^\circ or 2π2\pi radians

What is the definition of the secant function?

secθ=1cosθ\sec \theta = \frac{1}{\cos \theta}

Where does secθ\sec \theta have vertical asymptotes?

θ=90,270,450,\theta = 90^\circ, 270^\circ, 450^\circ, \dots

What is the period of the secθ\sec \theta function?

360360^\circ or 2π2\pi radians

What is the definition of the cotangent function?

cotθ=cosθsinθ\cot \theta = \frac{\cos \theta}{\sin \theta}

What is the period of the cotθ\cot \theta function?

180180^\circ or π\pi radians

How does the graph of cotθ\cot \theta behave between asymptotes?

It is a decreasing curve

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