General Solution of Trigonometric Equations (VCE SSCE Mathematical Methods): Quizzes

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General solution of trigonometric equations
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Why do trigonometric equations have infinitely many solutions?

Trig functions are periodic

What is the range of cos⁡−1\cos^{-1}?

[0,π][0, \pi]

What is the range of sin⁡−1\sin^{-1}?

[−π2,π2][-\frac{\pi}{2}, \frac{\pi}{2}]

What is the general solution of cos⁡x=a\cos x = a for a∈[−1,1]a \in [-1, 1]?

x=2nπ±cos⁡−1(a)x = 2n\pi \pm \cos^{-1}(a)

What is the general solution of tan⁡x=a\tan x = a for a∈Ra \in \mathbb{R}?

x=nπ+tan⁡−1(a)x = n\pi + \tan^{-1}(a)

What is the period of the tangent function?

π\pi

What is cos⁡−1(12)\cos^{-1}\left(\frac{1}{2}\right)?

π3\frac{\pi}{3}

What is sin⁡−1(−12)\sin^{-1}\left(-\frac{1}{2}\right)?

−π6-\frac{\pi}{6}

For equations with phase shifts, what should you do first?

Isolate the entire expression

What must always be specified when writing general solutions?

n∈Zn \in \mathbb{Z}

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