WEBVTT
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problem 16 asks us to evaluate. The six triggered
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a metric functions of Fada for part A and for
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part B. And one thing we can take advantage
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of when looking at this problem is the properties of
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CO terminal angles. SOCO terminal angles are angles that
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start and end of the same spot. So although
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this is ah to single right, it's co terminal
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angle is actually gonna be this acute angle right here
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. Same goes for this one. And this is
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nice for these questions because it might be a little
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daunting to think about our problem when looking at this
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huge of two single. But instead, we can
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just draw a nice triangle for this co terminal angle
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and then use those values to solve for our chicken
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metric functions. Sober party. Let's draw a right
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triangle for this line right here. Is that horizontal
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on the X axis and this is our theta Keiko
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terminal. With this Ray. Now we know that
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in the ex direction there's eight spaces. Okay,
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goes eight and then in the wind direction and drops
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down 15. Yeah, and then we can d'oh
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the Pythagorean theorem to figure out what this Ah,
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side over here. The site like this. So
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you would do eight squared Those 15 square equal C
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squared or C equals the square root of eight squared
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plus 15 squared. So take a second to figure
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out what that is. All right, so that's
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gonna be 17. So with all of our sides
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figured out, we can easily come over here and
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then right out with these. Ah, with these
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triggered a metric equations, they're going to evaluate too
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. So sign is the same as the opposite side
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over the high pot news. So 15 over 17
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co sign is the adjacent side over the abundance.
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That ratio is equal to cosign data. So have
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eight over 17. I pointed towards 15 but I
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meant 17 tangent is opposite over a Jason. So
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have 15 over eight now for our next three.
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They're just the reciprocal sze of these set up here
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. So co seeking is the reciprocal of sign,
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meaning that it's 17 over 15. Seeking is the
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reciprocal of co sign immunity. It's 17 over eight
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and co tension is the reciprocal of tangent, meaning
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it is eight over 15. All right, so
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that those are the six string metric functions for part
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A. So for a little a up here now
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moving on to be we're gonna do the exact same
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process. Okay, so let's create our right triangle
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with this being angle singles. Arteta. Now we
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know this side length is one. And this I
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like this one because it comes out one of the
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extraction and one in the wind direction. And that
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means that our hypotheses value when we do, our
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Pythagorean theorem of a squared plus B squared equals C
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squared. She's gonna be one squared too close to
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the top. One squared plus one square equals C
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squared. Right? See, being this high partners
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right here, we're gonna end up having C equals
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the square root of two, this one plus one
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. Now that we have all of our side links
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, you can come in and do the same thing
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we did over here. We can evaluate thes by
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looking at their ratios. So we have one over
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square root too. Coastlines going to be one over
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square to a swell tangent is going to be one
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over one, which equals one now. Coast seeking
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will be the reciprocal of sign seeking only the reciprocal
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of co sign and Coach Angel be their simple of
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one, which is also just one. All right
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. And there you have it. Those are the
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six geriatric functions for both values of theta.