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Joana S.

Experienced Math and MATLAB Tutor

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SAT II Mathematics Level 2

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Question:

As $$θ$$ increases from $$ \frac{π}{4} $$ to $$ \frac{5π}{4} $$, how do the values of $$ 4cos(\frac{1}{2}θ) $$ change? (increase/ decrease)

Joana S.

Answer:

Let's start by examining how $$ 4cos(\frac{1}{2}θ) $$ is different from $$ cos(θ) $$. The 4 is multiplied to every output of $$ cos(\frac{1}{2}θ) $$, so it must affect the amplitude. The amplitude change is not relevant to the question. The first period of $$ cos(θ) $$ is from 0 to $$ 2π$$. However, in $$ cos(\frac{1}{2}θ) $$, the first period starts at 0 but will end at $$ 4π$$ because: $$ cos(\frac{1}{2}(4π)) = cos(2π) $$ In other words, the $$ 4cos(\frac{1}{2}θ) $$ is stretched horizontally by a factor of 2, so this cosine graph will decrease until $$ 2π$$ and increase until $$ 4π$$. Therefore, the values of $$ 4cos(\frac{1}{2}θ) $$ will decrease as $$θ$$ increases from $$ \frac{π}{4} $$ to $$ \frac{5π}{4} $$

MATLAB

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Question:

How can I interpolate my data using MATLAB?

Joana S.

Answer:

Once you have your x and y data, use $$ polyfit $$ to fit the data to a polynomial: $$p = polyfit(x,y,n)$$ Where the $$p$$ returned contains the coefficients of the $$nth$$ order polynomial. Once you find a polynomial degree that gives a good fit, use $$ polyval $$ to find the y value for the x you wish to interpolate: $$y1 = polyval(p, x1)$$

College Admissions

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Question:

Writing isn't my strong suite, and I'm not sure what to write about in my college essays. What would you suggest?

Joana S.

Answer:

Everyone can write an amazing college essay! It's mostly about being honest, personal, and a little creative. My advice would be to write about an experience or person that has as impacted your life and shaped you into who you are today. If you're still stuck, be creative with what you choose to write about. It's not so much what you write about, but how it's told and what it says about who you are.

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