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University of California, Berkeley

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Problem 33

Solving a Trigonometric Equation In Exercises $31-34$ , find two solutions of each equation. Give your answers in radians $(0 \leq \theta \leq 2 \pi) .$ Do not use a calculator.

$$\begin{array}{l}{\text { (a) } \tan \theta=1} \\ {\text { (b) } \cot \theta=-\sqrt{3}}\end{array}$$

Answer

(a) $\theta=\frac{\pi}{4}$ or $\frac{5 \pi}{4}$

(b) $\theta=\frac{5 \pi}{6}$ or $\frac{11 \pi}{6}$

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## Discussion

## Video Transcript

okay, So far apart they were given the tangent of data is equal to one. Well, that means our opposite. It and our Jason sides are equal. Well, when is this positive brought up? When the variable for opposites and our case, insides are both one or when they're both negative. So then we either have It's being pyre before or five. I owe for now for part B. When it's Cho attended a beta equal to square root of three. Well, Coach, hand innovator is equal to one over tendency potato, which is equal tube and all right adjacent over opposite side being equal to the square root of three. But I mean, that tended Evita because the opposite over adjacent, which is equal to one over and they look square would agree The one of the, um well, that means there are opposite side could be positive. Just give us, and then our distance. I would have to be negative, so that would give me negative adjacent side and then positive opposite side. That would give me Let's see, however, six mm. By firing six. Yeah, that would give me five every six. Or that would mean that our opposite side is negative and in our days, inside is positive. So what we've been quoted for, which would give me a love and pie over six.

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