-1 is less than or equal to sine Theta, which is less than or equal to one. And -1 is less than or equal to cosine alpha which is less than or equal to one. And it doesn't matter what Theta and alpha are. So we can be way out on Infinity and have it be oscillating back and forth and know that we're still at a number in between -1 and one. So when we look at this problem, we're talking about the limit as T goes to negative Infinity of 3 -, 2 T plus sine 8 T divided by 5T plus cosine 8T if we took the highest term in the denominator and divided everything by the highest degree variable, in this case just a single T because that cosine 8 T is all together. So if I took and divided every term by T, I get 3 / t -, 2 plus sine eight t / t / 5 plus cosine eight t / t Now when we look at this 3 / a really, really big negative number 3 / -10 three over -103 / -1000 that's going to go to zero. It's going to get smaller and smaller and smaller. Sine 8 T -1 to one. It's somewhere in between -1 and one. It could also equal -1 or one. So a constant over a really, really big negative number is going to go to 0 and the denominator 5 plus cosine eight t / t that cosine 8 T. Once again, something between -1 and one could equal the endpoints over 10 negative 10, negative 100, negative 1000. So that's going to go to zero also. So we're going to get a final answer of -2 fifths.