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University of California, Berkeley

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Problem 31

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.

$$\begin{array}{l}{\text { (a) } \cos \theta=\frac{\sqrt{2}}{2}} \\ {\text { (b) } \cos \theta=-\frac{\sqrt{2}}{2}}\end{array}$$

Answer

(a) $\theta=\frac{\pi}{4}$ or $\frac{7 \pi}{4}$

(b) $\theta=\frac{3 \pi}{4}$ or $\frac{5 \pi}{4}$

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## Discussion

## Video Transcript

Okay, so we have co sign of data, which is a road of fuel to you. Could be right that as one over square root of two and then write a triangle. So we have co sign, which is ours s inside, which is one over my partner, which is square with it, too. Opposite side in. Very so it's either gonna be Let's see that our cases I have to be positive. So if you're gonna be in quadrant one or a Quadrant four. But we do have a channel here or here and then and then since, um, this is going to and this is one other side, half have to be the same length as our Jason side. So if you're gonna be negative, one are positively. But I give the theater fire before, which is in quadrant one or seven pie before. Thank you, Sergeant four. Okay, now we haven't closed on Abydos. Is it to make up for a vote of two over? But I think it's a negative one over square root of going that triangle out. We said that her Connie's always have to be positive. So only thing that is negative is our days inside. So we're gonna either be in Kuala Geant to her closet three because our opposites act very based on just given information. So this is gonna be either if we're in Quadrant three, three prior before or 55 before when Quadrant Pretty.

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