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# Tutor profile: Anna K.

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Anna K.
Yale University student, tutor for two years
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## Questions

### Subject:Trigonometry

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Question:

In right triangle $$EFG$$, $$\tan(E)$$ is 4/3. What are $$\sin(E)$$ and $$\cos(E)$$?

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Anna K.

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

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Question:

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?

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Anna K.

### Subject:ACT

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Question:

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?

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Anna K.

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