Reciprocal Trig Functions - Definitions (Edexcel A-Level Mathematics): Quizzes

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Reciprocal Trig Functions - Definitions
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What is the definition of csc⁡θ\csc \theta?

1sin⁡θ\frac{1}{\sin \theta}

Which expression is equivalent to cot⁡θ\cot \theta?

cos⁡θsin⁡θ\frac{\cos \theta}{\sin \theta}

At which angles is sec⁡θ\sec \theta undefined?

90°,270°90°, 270°

When is csc⁡θ\csc \theta undefined?

When sin⁡θ=0\sin \theta = 0

What is the range of sec⁡θ\sec \theta?

(−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty)

How does the graph of cot⁡θ\cot \theta behave as θ\theta increases?

It decreases

Which identity relates sec⁡2θ\sec^2 \theta and tan⁡2θ\tan^2 \theta?

sec⁡2θ=1+tan⁡2θ\sec^2 \theta = 1 + \tan^2 \theta

What is the Pythagorean identity for csc⁡2θ\csc^2 \theta and cot⁡2θ\cot^2 \theta?

csc⁡2θ=1+cot⁡2θ\csc^2 \theta = 1 + \cot^2 \theta

What is the simplified form of csc⁡θ⋅sin⁡θ\csc \theta \cdot \sin \theta?

11

If tan⁡A=13\tan A = \frac{1}{3}, what is sec⁡2A\sec^2 A?

109\frac{10}{9}

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