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University of California, Berkeley

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Problem 17

Evaluating Trigonometric Functions In Exercises $17-20$ , sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ . Then evaluate the other five trigonometric functions of $\theta$ .

$$\sin \theta=\frac{1}{2}$$

Answer

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## Discussion

## Video Transcript

Okay, Well, given that sine of data is, he could feel 1/2. So drawing out that triangle, you know that opposite is one. And hi, pop music too. So now we just need to find this term on the bottom so we can use our people agree and dim. You know that R squared is equal to x squared. Plus y quite you know that. Why is one that's one squared plus x squared? Because our word, which is two squared, which is what? So we have four minutes one x squared, which means that X is equal to the square root of three. Okay, so this is clearly a defeat so that we can find a other angles. So we know that coastline of data. The people here, Jason over. Hi, Panis. Tangents of data he could to opposite over adjacent anything. My pockets are not over opposite Beacon of data is about a typical of co sign that's two over square root of B. And speaking of data is difficult off sign, which is to over one

## Recommended Questions

Evaluating Trigonometric Functions In Exercises $17-20$ , sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ . Then evaluate the other five trigonometric functions of $\theta$.

$$\cos \theta=\frac{4}{5}$$

Evaluating Trigonometric Functions In Exercises $17-20$ , sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ . Then evaluate the other five trigonometric functions of $\theta$.

$$\sin \theta=\frac{1}{3}$$

Evaluating Trigonometric Functions In Exercises $17-20$ , sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ . Then evaluate the other five trigonometric functions of $\theta$.

$$\sec \theta=\frac{13}{5}$$

In Exercises 13-20, sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of $\theta$.

sin $\theta = \frac{1}{5}$

In Exercises 13-20, sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of $\theta$.

tan $\theta = \frac{4}{5}$

Sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta .$ Use the Pythagorean Theorem to determine the third side of the triangle and then find the values of the other five trigonometric functions of $\theta$. $$\csc \theta=\frac{17}{4}$$

In Exercises 13-20, sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of $\theta$.

sec $\theta = \frac{17}{7}$

Given the following information about one trigonometric function, evaluate the other five functions.

$\sin \theta=-\frac{4}{5}$ and $\pi < \theta < 3 \pi / 2$ (Find $\cos \theta, \tan \theta, \cot \theta, \sec \theta$ and $\csc \theta .)$

Use the given value of a trigonometric function of $\theta$ to find the values of the other five trigonometric functions. Assume $\theta$ is an acute angle.

$$\tan \theta=\frac{1}{2}$$

Sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$. Use the Pythagorean Theorem to determine the third side and then find the values of the other five trigonometric functions of $\theta$

$\tan \theta=2$