Question

Please help me understand how to solve this questions. I need step by step solution and answer because I find it difficult to understand when someone on here writes the answer instead of showing step by step work on how he/she got the numbers to get the answers. I know I'm asking for too much, but I want to learn it. I want to understand it so when I take a test in the future, I won't find it challenging. THANK YOU SO MUCH!.

1) Determine the​ quarter points of
y=−cos(2x−π)

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2) Find the quarter points of y=-3sin(-x+π/2)

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3) Find the quarter points of y=3cos(4x+π)+1

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4) Find the quarter points of
y=2-3cos(4x-π)

(Simplify your answers. Type ORDERED PAIRS. Type exact answers, using π as needed. Use integers or fractions for any numbers in the expressions)

Answer 1

what you really need to know is that the period of cos(kx) is 2π/k.

Then just divide that length into 4 intervals, and evaluate y at each dividing point.

For example,

3cos(4x+π)+1 has period 2π/4 = π/2.
Thus, each quarter has length π/8.

So, the points are
(0,-2)
(π/8,0)
(π/4,4)
(3π/8,0)
(π/2,-2)

Of course, you might want to shift that so it starts at its maximum, the way cos(x) does. In that case, note that

cos(4x+π) = cos(4(x + π/4))
So, you need to shift left by π/4, so the quarter points would be

(-π/4,4)
(-π/8,0)
(0,-2)
(π/8,0)
(π/4,4)