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University of California, Berkeley

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Problem 19

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 $\theta$.

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

Answer

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## Discussion

## Video Transcript

Okay, so we're given coastline of data, is good for over five and were asked to find the rest of the angles. Well, we know that speaking of data, just the reciprocal of Cosette, a bitter set up five over four and for the very meaning we need to find our right triangle between a close, an idea is opposite or not upset. Jason set up, pour over hypotheses. So we need to find the opposite side bar angle. So it seems you've got a degree in dim that's r squared is equal to x squared plus y squared. So we have X is four squared plus y squared is because our square, which is five squared. That's 25 minus 16 people to wife Quite. Which gives me dad the square root of nine. Because wine and why is equal to okay, Okay, you know we have there beside, so it Look for a sign and beta, It's all over. Pardon me, Canyon. A video which is opposite over adjacent coach engine of data. The reciprocal tangent. That's for three. And co Speaking of data, which is typical of signs which is five over three

## 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 $\theta$.

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

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 $\theta$ .

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

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 $\theta$.

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

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 $\theta$. $$\csc \theta=\frac{17}{4}$$

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 $\csc \theta .)$

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 $\theta$.

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

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.

$$. \tan \theta=5$$

In Exercises $9-16,$ 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 other five trigonometric functions of $\theta$ .

$$

\csc \theta=\frac{17}{4}

$$