Explanation for Question 36 From the Math (Calc) Section on the Official Sat Practice Test 8
So in question number 36, we're given a triangle and within this triangle where 2 we're told that we have a point w which lies on the line RT 3 right here. So I can put a point w right here, 4 and you can go anywhere on that line. And then we're told the angle 5 RSW. So right here, 6 we'll call that angle. A and then we're told also to look at the 7 sine of angle, w S T right, 8 w S T we'll call that angle B. 9 And so the important thing to notice about these angles is that they're complimentary 10 angle, a plus angle B will be equal to 90 degrees, 11 and there's a special relationship when you have complimentary angles and you're taking their 12 sign in their co-sign. And what it means is that the co-sign of angle 13 a is going to be equal to the sine of angle B one a 14 and B are complimentary. 15 And the best way to think about this perhaps is with an example. 16 So let's take the example of a pair of angles that are 30 degrees 17 and 90 degrees. And these are complimentary or 30 degrees and 60 18 degrees. I'm sorry. Um, and they're complimentary because when I add them together, 19 I get 90 degrees. Now, if you plug sine of 30 into your calculator, 20 you get one half. And if you plug co-sign of 60 into your calculator, 21 you also get one half, right? So taking the sign of one of the 22 angles will give you the same answer as if I take the co-sign of 23 the other angle. And so knowing that the sign and the co-sign are going 24 to be the same thing, if I'm subtracting them, 25 my answer should be zero. Right? 26 For example, if we use this one half, I would be doing one half 27 minus one half, which is zero. So no matter where you put the point 28 w on that line, your answer would be zero.