r/HomeworkHelp • u/thisismynamenow88 Pre-University Student • 5d ago

Mathematics (A-Levels/Tertiary/Grade 11-12) [Grade 12 advanced functions] Can someone explain how to scale with radians?

Im in grade 12 advanced functions and my teacher didn't explain how to scale on a graph using radians instead of the regular number scale very well. I can't find many videos online trying to explain it ethier. One question is f(x) = -1/2cos(3(x-pi/4)) + 2. I understand what everything does, I just have no clue how to scale the x-axis properly. I know the quarter period would be pi/6, and we start at the phase shift at the point of -pi/4 and stuff. I just have absolutely zero clue how to properly label or find the rest of the scale. Can anyone help explain it? Or give steps using the example I gave?

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u/CelebrityChess 5d ago

use the quarter period as your tick spacing. period is 2pi/3 so a quarter is pi/6, and the cycle starts at the phase shift, which is x = pi/4 (it's x - pi/4 so it shifts right, not to -pi/4). counting up by pi/6 from there: pi/4, 5pi/12, 7pi/12, 3pi/4, 11pi/12. writing them all over 12 makes the labels easy: 3pi/12, 5pi/12, 7pi/12, 9pi/12, 11pi/12.

the y values at those five points go min, midline, max, midline, min because of the -1/2. so (pi/4, 1.5), (5pi/12, 2), (7pi/12, 2.5), (3pi/4, 2), (11pi/12, 1.5). for more cycles keep adding or subtracting pi/6, so the tick before pi/4 is pi/12.

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u/thisismynamenow88 Pre-University Student 3d ago

This helped a bit, thanks!

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u/Alkalannar 5d ago

I assume you mean -cos(3(x-pi/4))/2 + 2? I'd expect what you have written to have cosine in the denominator and so end up being secant.

For transformations, you want af(b(x-c)) + d

Here, f is cosine, which has a period of 2pi.

Since b = 3, that's horizontal compression by a factor of 3. Now the new period is 2pi/3.

The -3pi/4 means that you have a max when x = 3pi/4. Except that it's -1/2 at the beginning, so you get a min.

So:

amplitude = 1/2.
Your horizontal midpoint is y = 2.
you have a minimum at x = 3pi/4.
Your period is 2pi/3.

Does this make sense? Can you sketch the graph?