Trigonometric Functions (Leaving Cert Mathematics): Quizzes

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Trigonometric Functions
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What is the Pythagorean identity relating sin⁡2θ\sin^2 \theta and cos⁡2θ\cos^2 \theta?

sin⁡2θ+cos⁡2θ≡1\sin^2 \theta + \cos^2 \theta \equiv 1

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

tan⁡2θ+1≡sec⁡2θ\tan^2 \theta + 1 \equiv \sec^2 \theta

What is the double angle identity for sin⁡2θ\sin 2\theta?

2sin⁡θcos⁡θ2 \sin \theta \cos \theta

Which is NOT a form of cos⁡2θ\cos 2\theta?

2sin⁡2θ+12\sin^2 \theta + 1

What is ∫tan⁡2θ dθ\int \tan^2 \theta \, d\theta?

tan⁡θ−θ+c\tan \theta - \theta + c

What is ∫tan⁡θ dθ\int \tan \theta \, d\theta?

−ln⁡∣cos⁡θ∣+c-\ln |\cos \theta| + c

What is ∫sin⁡2x dx\int \sin^2 x \, dx?

12x−14sin⁡(2x)+c\frac{1}{2}x - \frac{1}{4} \sin(2x) + c

What is ∫cos⁡2x dx\int \cos^2 x \, dx?

12x+14sin⁡(2x)+c\frac{1}{2}x + \frac{1}{4} \sin(2x) + c

What is ∫sin⁡θcos⁡θ dθ\int \sin \theta \cos \theta \, d\theta using the double angle formula?

−14cos⁡2θ+c\frac{-1}{4} \cos 2\theta + c

To integrate sin⁡2x\sin^2 x, what should sin⁡2x\sin^2 x be written as?

12−12cos⁡2x\frac{1}{2}-\frac{1}{2}\cos2x

What is the identity for tan⁡θ\tan \theta?

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

What is ∫tan⁡3x dx\int \tan^3 x \, dx?

13tan⁡3x−tan⁡x+x+c\frac{1}{3}\tan^3 x - \tan x +x+c

What is the standard integral ∫sin⁡(x) dx\int \sin(x) \, dx?

−cos⁡(x)+C-\cos(x) + C

Which identity relates cot⁡2θ\cot^2 \theta and csc⁡2θ\csc^2 \theta?

1+cot⁡2θ≡csc⁡2θ1 + \cot^2 \theta \equiv \csc^2 \theta

What is ∫cos⁡2(10x) dx\int \cos^2 (10x) \, dx?

140sin⁡(20x)+12x+c\frac{1}{40}\sin (20x)+\frac{1}{2}x+c

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