Trigonometric Functions (Leaving Cert Mathematics): Flashcards

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Trigonometric Functions
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Identity: sin⁡2θ+cos⁡2θ=?\sin^2\theta + \cos^2\theta = ?

11

Identity: tan⁡2θ+1=?\tan^2\theta + 1 = ?

sec⁡2θ\sec^2\theta

Identity: 1+cot⁡2θ=?1 + \cot^2\theta = ?

csc⁡2θ\csc^2\theta

Identity: sin⁡2θ=?\sin 2\theta = ?

2sin⁡θcos⁡θ2\sin\theta\cos\theta

Identity: cos⁡2θ\cos 2\theta in terms of cos⁡2θ\cos^2\theta

2cos⁡2θ−12\cos^2\theta - 1

∫sin⁡(x)dx=?\int \sin(x) dx = ?

−cos⁡(x)+C-\cos(x) + C

∫tan⁡2θdθ=?\int \tan^2\theta d\theta = ?

tan⁡θ−θ+c\tan\theta - \theta + c

∫tan⁡θdθ=?\int \tan\theta d\theta = ?

−ln⁡∣cos⁡θ∣+c-\ln|\cos\theta| + c or ln⁡∣sec⁡θ∣+c\ln|\sec\theta| + c

Step 1 to integrate sin⁡2x\sin^2 x or cos⁡2x\cos^2 x

Expand cos⁡2x\cos 2x in terms of the function

∫sin⁡2xdx=?\int \sin^2 x dx = ?

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

∫cos⁡2xdx=?\int \cos^2 x dx = ?

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

Simplify sin⁡θcos⁡θ\sin\theta\cos\theta using double angle

12sin⁡2θ\frac{1}{2}\sin 2\theta

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