Explanation for Question 9 From the Math (No Calc) Section on the 2020 October Sat
So question number nine, draws out a triangle for us. 2 And they tell us that the sine of X is five over eight, 3 and they want us to find out what the co-sign of Y is. 4 So now if we're trying to do this, we can see that sign of 5 X sine is opposite over hypotenuse, 6 always. And so if we look at the angle of X, 7 we can see that the opposite side is the side. 8 And if five over eight is opposite over hypotenuse. 9 So that means that our opposite side is five. 10 Again, this is our opposite side. It's directly across from X. 11 So this side length will be five. And then our hypothesis is eight and 12 the hypothesis is always the diagonal longest side of the triangle. 13 Or you can think about the hypothesis being opposite, 14 the right angle. And so this side is going to be eight. 15 So now we can see, okay, if I want to find the co-sign of 16 why my angle, 17 why is right here in the pink. 18 And I know that co-sign is adjacent, over-hype hot news, 19 then I need to figure out what the adjacent side of why is C 20 the side right next to why is five? And then my hypotenuse is 21 eight. That one doesn't change. And so my co-sign of Y is actually going 22 to be the same as my sine of X. 23 And that'll give me C and so you can always do this by the 24 math, but this is also a pattern in, 25 um, in trigonometry that the side of one angle is the same 26 as the co-sign of its complimentary angle. 27 And so either way, either by the logic of it or by the math, 28 you can get the answer choice C.