Haven't learned half the stuff on the SAT

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SeventhSandwich:
For the first one, look at the graphs of sin(x) and cos(x). If you notice, they're the same thing but sin(x) is just cos(x), but phase-shifted +90 degrees. (It's 90 degrees 'ahead' of cos(theta).

If you think about cos(90 - x), what that's really saying is 'take cos(x), shift it 90 degrees to the left, and then flip it over the y-axis'. If you draw out cos(x) and do this, you'll quickly notice that the graph you get is the exact same thing as sin(x). Thus, cos(90-x) = sin(x) = 4/5, as given in the question.

Second one is just algebra.
R = F / (N + F)

We want an equation that says F = <the rest of the stuff>

so we do this:
R(N+F) = F
RN + RF = F
RN = F - RF
RN = F(1-R)
RN/(1-R) = F

So answer B.

The third question is a quadratic equation question. You have basically two options for how to deal with these: either google how to make a calculator program that will solve the roots for you, or memorize the equation.

For functions that look like ax^2 + bx + c = 0, there are generally only one or two values of 'x' that when you plug them into the left-hand side of the equation, it comes out equaling zero. To find them, you use the quadratic formula

https://www.youtube.com/watch?v=2lbABbfU6Zc

(it's a patronizing song but it works)

By doing this, you get two roots: 4 - 2*sqrt(3) and 4 + 2*sqrt(3). Add them both together and you get 8.

Sheepocalypse:

--- Quote from: Aide33 on April 04, 2017, 05:47:42 PM ---yeah i find actually drawing a triangle helps students understand trig a lot more than just equations pulled out of seemingly thin air, but to each their own

--- End quote ---
I don't think I personally would have enough time to draw something.

Sheepocalypse:
thanks for the help though, guys

SeventhSandwich:

--- Quote from: Sheepocalypse on April 04, 2017, 06:03:50 PM ---I don't think I personally would have enough time to draw something.

--- End quote ---
It doesn't take that long, and it's arguably easier than transforming triangles and other weird stuff. Here, I drew a picture of the thought-process I used.

Nonnel:
first is trig which i don't get at all but the other two are just algebra

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