Use the given point on the terminal side of angle θ to find...

Use the given point on the terminal side of angle $\theta$ to find the value of the trigonometric function indicated. 9) $\tan \theta$ $\tan \theta = \frac{3}{9} = \frac{1}{3}$ 10) $\cos \theta$ $\cos \theta = \frac{20}{20\sqrt{2}} = \frac{1}{\sqrt{2}}$ 11) $\cos \theta$ 12) $\tan \theta$; (9, 18) 13) $\tan \theta$; (4, 3) 14) $\cos \theta$; $(8, \sqrt{17})$

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00:01 So from this problem, it's unclear, to mean the specifics of it.

00:06 So i'm going to go through an example of a general example, and maybe the exact point you have in your homework or whatever you're going through.

00:18 You can use this as a guide.

00:20 So if we were to say have 0 .34, and we wanted to draw a line to it.

00:36 Okay, the terminal side of the angle, right, we're circling from zero to this point.

00:43 So the terminal side ends up being this line, and then the initial side is going to end up being the x -axis, so we have our angle theta here.

00:54 Okay, so maybe we could put it in blue, it would be the terminal side.

01:00 And we can also sort of imagine a vertical line, you know, on the initial side, the x -axis, and orthogonal to the x -axis here.

01:15 Or perpendicular.

01:17 And so what we know is we can figure out the length of all the sides of the triangle.

01:24 Okay, so we know that opposite the angle here is going to be a four, because that's our y value.

01:32 The length along the x -axis is three.

01:35 We know that we have this point here.

01:41 Okay, and if we use the pythagorean theorem to figure out the length of the terminal side, we will get a five.

01:51 So it's going to be the square root of 3 squared, which is 9, plus 4 squared, which is 16.

01:57 It would give us the square root of 25.

02:01 So now if you want to figure out trig functions, perhaps you know this sokatoa, that's how i was taught it, right? which means sine is equal to opposite over hypotenuse...

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