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Problem 39

Solving a Trigonometric Equation

In Exercises $35-42$ , solve the equation for $\theta,$ where $0 \leq \theta \leq 2 \pi$

$$\sec \theta \csc \theta=2 \csc \theta$$

Answer

$\theta=\frac{\pi}{3}, \frac{5 \pi}{3}$

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## Discussion

## Video Transcript

Okay, so we are seeking a bitter time classic in the data is he could to court seeking a better. If you eat that as one over co sign of there Times one over sign of data you could to over one, uh, one oversight of there. Well, we can multiply by side of there on both sides to would cancel. So we're left with one over co sign a beta because too what? Well, that means that cola sign of their people to 1/2 and close. The elevator is equal to 1/2 when data is equal to pi over three or when it's five pi over drinks.

## Recommended Questions

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Solving a Trigonometric

Equation In Exercises $35-42,$ solve the equation for $\theta,$ where $0 \leq \theta \leq 2 \pi .$

$$\tan ^{2} \theta=3$$

Solve for the angle $\theta,$ where $0 \leq \theta \leq 2 \pi$.

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Solve for the angle $\theta,$ where $0 \leq \theta \leq 2 \pi$.

$$\sin 2 \theta-\cos \theta=0$$

In Exercises 37-46, use trigonometric identities to transform the left side of the equation into the right side $(0 < \theta < \pi /2)$.

$\frac{sin\ \theta}{cos\ \theta}$ $+$ $\frac{cos\ \theta}{sin\ \theta}$ $=$ $csc\ \theta\ sec\ \theta$

Solve the given trigonometric equation exactly on $0 \leq \theta<2 \pi$.

$$\tan ^{2} \theta-\sqrt{3} \tan \theta=0$$