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0 41 1. Score: (Type 302 Evaluate LL" an sin 41 of Homework: exact . 09 | 8 pt sin answer; 8 0 (e2) 00 using 8 4 as needed:)...

Question

0 41 1. Score: (Type 302 Evaluate LL" an sin 41 of Homework: exact . 09 | 8 pt sin answer; 8 0 (e2) 00 using 8 4 as needed:)

0 41 1. Score: (Type 302 Evaluate LL" an sin 41 of Homework: exact . 09 | 8 pt sin answer; 8 0 (e2) 00 using 8 4 as needed:)



Answers

In Exercises $31-46,$ find the exact value of each expression, if possible. Do not use a calculator. $$\sin \left(\sin ^{-1} 0.9\right)$$

In this case, I'm looking for the sign of nine pi over four to double check to see whether this is more than one rotation. I'm going to look at the value to pie. Two. Pi is the same as eight pi over four for using a common denominator since nine. Power force greater than eight pi over four. If I take away one rotation nine pi over four minus eight pi over four will result in the sign of pi over four. Sign a pi over four is in the first rotation and in the first quadrant pi over four would be your reference angle making the sides route to over two for each being an isosceles right triangle. The sign is your height. So the answer to this problem is Route two over.

This problem. We're looking to evaluate the sign of negative nine pi over four. We're going to compare this to two pi to see if it's in the first rotation. Kevin, a common denominator of 42 pies equivalent to a pi over four nine pi over four is more than that. So in this case, we're gonna take negatives. Nine pi over Forge, which just tells you the rotation will be clockwise and we're gonna go back one full rotation. So we're gonna add eight pi over Forks. We're gonna go counterclockwise to pie sign. Will then be negative pi over four, which is a rotation clockwise in the fourth quadrant. This will have a reference angle of pi over four, which makes this an isosceles right triangle, which tells me that the sides are route to over to Since it's in the fourth quadrant, the height will be negative and the width will be positive. Sign is looking for the height. So the answer to this problem is negative. Route to over to

Okay, so this problem, uh, give us a list of ice perfects, And it wants us to create a table of values for plugging in, uh, ex into effort backs because the inverse sine of that value X plus the coastline Inverse co sign of X. Okay, so the interesting thing. Well, what's What's better value? So we have zero. We're gonna have one, huh? Whenever it to over two, 3/2 one. Negative one, huh? Negative route to over two negative. Route 3/2. Negative. Now, the interesting thing here is, if we have forgiven those ratios, then, uh, whatever the sign, value and co sign values will be. The angles for these triangles will just be obstinate signs. So one day there will be one side. The other thing, it will be the other. Because sign would be opposite Ever had partners and cause I would be a Jason ever happened news. So we're gonna be talking about opposite angles of a right triangle. So if we add those two angles So it was called State of Wanted to, uh, they didn't one plus stated to We'll always give us on nine degrees, just kind of the rule for the other two angles of a right triangle in radiance is just gonna be a pie over to every single one of these. Unless it has a domain error, which none of them do because they're all between negative one and positive One, uh, half of these values of acts is always gonna be a pie over too. Yeah, and that's that's really it. So every single one of these sine inverse plus coast on inverse will always give pie or two or 90 degrees whichever way you want to think about it. Uh, thank you.

The first thing you want to do is make sure your calculator is set to radiant mode. And then to find inverse sign, you use the second function of your sign button. So second sign and we're finding the inverse sign of 0.31 and then rounding our answer to two decimal places, we get 20.3 to radiance.


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