In right triangle $$EFG$$, $$\tan(E)$$ is 4/3. What are $$\sin(E)$$ and $$\cos(E)$$?
This question uses the 3-4-5 triangle (a right triangle in which one side has a length of 3, one side has a length of 4, and one side has a length of 5), a triangle that is used very often in trigonometry questions and on standardized tests. First, draw out the problem. This always helps with understanding what the question is asking and what information you're given. Because the 3-4-5 triangle is easy to work with, we will draw this triangle with the legs (the sides touching the right angle) having lengths of 3 and 4. Now, because of $$tan(E)$$ = the side opposite angle $$E$$ / the side adjacent to angle $$E$$, we can label the angle between the hypotenuse and the leg with a length of 3 as angle $$E$$. Next, using what we know about 3-4-5 triangles or the Pythagorean theorem, we can figure out that the hypotenuse has a length of 5. Now that we have a triangle drawn and all sides labeled, finding $$\sin(E)$$ and $$\cos(E)$$ is simple. $$\sin(x)$$ = opposite/hypotenuse, so in this case $$\sin(E)$$ = 4/5 $$\cos(x)$$ = adjacent/hypotenuse, so in this case $$\cos(E)$$ = 3/5
I am trying to decide which colleges to apply to and have a list of over 20 schools. How can I narrow down my options and find the best college for me?
First, it's good that you have found so many schools that you like and have a solid list! You do want to narrow this list down, though, because applying to too many schools will only create unnecessary stress and decrease the quality of each application. There are several ways to narrow this list down: 1) Make sure that each school has the things that you need. Does it have the major or group of majors that you're considering? Is its financial aid policy likely to be sufficient for your family? 2) Think critically about fit. There are thousands of colleges in the United States and even more abroad, so there's going to be a college out there that will give you the opportunities and environment that will help you have a successful college experience. Some things to consider when evaluating a college's fit include setting (urban vs rural), size, academic atmosphere, social opportunities, and distance from home. Try to eliminate schools that don't fit your wants and needs. 3) Consider selectivity. Your college list should have about 3 schools you're pretty sure you'll be accepted by, 3 schools that are good matches, and 3 more selective schools that you're less likely to be accepted by. If your list is heavier on one of these three categories, try to narrow those schools down. 4) If you can, visit. Visiting colleges, especially ones far away, can be difficult for financial and time reasons, but a visit can have a dramatic effect on your feelings for a school. During my college search, I visited several schools that I was seriously considering attending and walked away certain that I wouldn't apply. It's best to visit when the academic year is underway so you can see and talk to current students, but walking around campus any time of year will help you to visualize what it would be like as a student there.
I am struggling with the time limit on the math section of the ACT. How can I get through the test more efficiently while still being accurate?
The math section can be really difficult, time-wise. One thing that will help a lot is remembering that each correct answer is worth the same amount, no matter where it is on the test or how difficult the question is. Getting number 49 right will be worth just as much as getting number 3 right. With this in mind, you can move through the ACT math section much more quickly AND earn more points. A very effective strategy for the ACT math section is to complete the test in multiple rounds designed to make sure you get every point you possibly can. Your first time going through the section, you should answer any questions that you know how to do quickly and accurately. Make sure to clearly mark any questions you don't answer in the first round so that you don't miss them on your next pass through the test. The next time you go through the math section, you should answer the questions you know how to do but will take you longer. Still, skip over the questions you are less confident on and will take you a significant amount of time. Lastly, spend any remaining time on the most difficult questions. It is absolutely essential that you remember to bubble in a guess for each of these questions before the time is up. Because you won't be penalized for an incorrect answer, guessing will only help you. Using this strategy of going through the test in multiple rounds will help you to ensure that you answer every question you know how to do in the most time-effective manner possible!