Solving Trig Equations (Leaving Cert Mathematics): Quizzes

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Solving Trig Equations
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What does solving trigonometric equations involve finding?

All values of xx in specified domain

Which three tools are used in solving trig equations?

Identities, inverse functions, symmetry

What is Step 1 when solving trigonometric equations?

Isolate the trigonometric function

Which inverse functions are mentioned in Step 2?

sin⁡−1,cos⁡−1,tan⁡−1\sin^{-1}, \cos^{-1}, \tan^{-1}

What does Step 3 require you to account for?

Periodicity of the trig function

Which identity is specifically mentioned in Step 4?

sin⁡2x+cos⁡2x=1\sin^2x + \cos^2x = 1

What must you do in Step 5?

Verify solutions in specified domain

What are the solutions to sin⁡x=12\sin x = \frac{1}{2} in [0,2π][0, 2\pi]?

π6,5π6\frac{\pi}{6}, \frac{5\pi}{6}

What tool is used to find angles where sin⁡x=12\sin x = \frac{1}{2}?

The unit circle

What is the factorised form of 2cos⁡2x−cos⁡x−1=02\cos^2x - \cos x - 1 = 0?

(2cos⁡x+1)(cos⁡x−1)=0(2\cos x + 1)(\cos x - 1) = 0

For cos⁡x=−12\cos x = -\frac{1}{2} in [0,2π][0, 2\pi], what are the solutions?

2π3,4π3\frac{2\pi}{3}, \frac{4\pi}{3}

What is the complete solution to 2cos⁡2x−cos⁡x−1=02\cos^2x - \cos x - 1 = 0 in [0,2π][0, 2\pi]?

0,2π3,4π30, \frac{2\pi}{3}, \frac{4\pi}{3}

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