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University of California, Berkeley

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Problem 69

Think About It You are given the value of tan $\theta$ . Is it possible to find the value of sec $\theta$ without finding the measure of $\theta ?$ Explain.

Answer

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## Discussion

## Video Transcript

Okay, So if we're given, speaking of data is impossible to find over given tangent, and it is impossible to find. Is the seeking a better without murdering finding the milieu? Well, we don't think you know better to one over coast on Evita. Quibble started has taken square to beta. If you could do one over co sign squared up. Well, one is equal to co sign squared of data plus sign quite a bit over close in Cordoba. That was split in two. All right, listen. You two factions get seeking squared of theta is equal to co sign squared data over coastline. Quite a vato. Fine. Quit again. Well, the co sign squared is that that would give a secret squared from data is equal to one tended quarter better. Which would mean that seeking data can be found using square root of one plus tensions quite a bit

## Recommended Questions

THINK ABOUT IT You are given only the value $tan\ \theta$. Is it possible to find the value of $sec\ \theta$ without finding the measure of $\theta$? Explain.

You are given the value of tan $\theta .$ Is it possible to find the value of $\sec \theta$ without finding the measure of $\theta ?$ Explain.

If we know the value of $\sin \theta,$ is it possible to find the other five trigonometric function values? If not, what other information is needed?

Give the degree measure of $\theta$ if it exists. Do not use a calculator. See Example $3 .$

$$\theta=\tan ^{-1} \sqrt{3}$$

Give the degree measure of $\theta$ if it exists. Do not use a calculator. See Example $3 .$

$$\theta=\sin ^{-1} 2$$

Give the degree measure of $\theta$ if it exists. Do not use a calculator. See Example $3 .$

$$\theta=\cos ^{-1}(-2)$$

Give the degree measure of $\theta$ if it exists. Do not use a calculator. See Example $3 .$

$$\theta=\arctan (-1)$$

Give the degree measure of $\theta$ if it exists. Do not use a calculator. See Example $3 .$

$$\theta=\sec ^{-1}(-2)$$

Give the degree measure of $\theta$ if it exists. Do not use a calculator. See Example $3 .$

$$\theta=\csc ^{-1}(-2)$$

Give the degree measure of $\theta$ if it exists. Do not use a calculator. See Example $3 .$

$$\theta=\csc ^{-1}(-1)$$