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Problem 18

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 $\theta$.

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

Answer

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## Discussion

## Video Transcript

all right. So question Number 18 asks us to sketch a right angled triangle corresponding to the Trigana metric function of the acute angle data. Then evaluate the other five children a metric functions of data. So let's start by sketching that right triangle. Put that right there to indicate it's 90 degrees. Then I want to say that it is up here. Now when we look at this expression we've been given, synthetic was 1/3. We know that this 1/3 is a ratio of side lengths. So for sign, that's going to be the opposite. Sign the side opposite our angle over the high pot news. Okay, Now, if we want aside this up, if we want to find this other side be, let's say we're gonna have to do the Pythagorean theorem, which is a squared plus B squared equals C squared where this side of sea and this side is Hey, so we have one. Let's be squared equals three squared, which is nine. So I have B squared equals nine minus one, which is eight b equals the square root of a which can be simplified, but we got to 4 to 2 just seeing what we can factor out. We can fact around it to. Which leaves us with two square root too. As this side over here being now that we have found all three sides, we can easily express the other five. You're gonna metric functions of this acute angle theta as this ratios between these sides so well say co sign Fada equals tangent, data equals and we'll have seeking Veda equals co seeking theta equals tangent. Data equals Let's put our answers in green. So the coastline of the single is simply gonna be the adjacent sign over the high pot News or two square root to over three tangent is gonna be the opposite side over the adjacent side of that angle. One over two square two Now seek in. It's simply going to be the reciprocal of coastline. So we'll have three over two square two Coast seeking will be the reciprocal of Sign A three and then co tangent will be the reciprocal A tangent. A two square root too. And there you have it. These are the five other triggered a metric functions for the acute angle data

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