### Evaluating Trigonometric Functions In Exerrises $… 03:03 University of Southern California Problem 20 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\$.
$$\sec \theta=\frac{13}{5}$$

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## Video Transcript

and this problem asks us to sketch a right triangle, as I've done here below, Corresponding to this triggered a metric function. So you can't Dany equals 13 over five, and then with his information, we're supposed to evaluate, um, the other five tricking a metric functions, so C can't data is equivalent 21 over CO st Data. When I write this down, just because we know that coastline theta is the same as the adjacent side of our triangle over the high pot means because this is the reciprocal this simplifies right on down to C can't data equals high pot news over Jason. Now we look over here what we've been given, and we see that 13 is in the numerator where I hide pot nooses and five is in the denominator which represents our adjacent sideline. So we can come in and then just write that endure triangle now to solve for the opposite side, we can simply use of the factory and fear Um, given that excuse me, 13 squared equals five squared plus a square saying, given that the scientist, eh, Now a squared equals 13 squared minus five squared, which is the same as 144 and we know that 144 is a perfect square, meaning that a equals 12. And so once we've found all three side lengths, it's very simple to just come in here and then write down what are other five triggered? A metric functions are so co sign is adjacent overhype oddness. So that's five over 13 just like in the adjacent side. Over the high pot Nous sign is opposite over high pot news, so we look at the opposite side to this angle. Phaeton, which is 12 over 13 tangent, is the same as opposite over adjacent, so you can write 12 over five. Coast seeking is simply the reciprocal of Sign so that be 13 over 12 and co tangent is the reciprocal attention. So that would be five over 12. And there you have it. We've evaluated all five other tricking a metric functions, and now I'm done sharing