Question

How to sketch trigonometric graph without calculator?

Answer 1

Sketch the graph of f (x) = sin 3x + sin 6x, 0 ≤ x ≤ 2π

Answer 2

I have an idea but it is quite complicated to draw. you can try to find f'(x) and f''(x). equate them to zero and find any max/min points and inflection points. then try to draw a chart for range between 0 and 2pie, dividing this range into different ranges according to your max/min points and inflection points. lets say max and min points are x= A and B, B>A. so maybe you can divide your range to 0 to A, A to B, B to 2pie. but definitely consider all the max/min and inflection points. For these ranges, determine the value of f'(x) and f''(x) which means within 0 to A, A to B and B to 2pie regions whether it's positive or negative value for f'(x) and f''(x). If f'(x) positive, means that it's an increasing trend in this region; if negative means decreasing. For f''(x), positive means the graph within this region should be concave upwards; negative means concave downwards. I think it should work if you draw it this way.

Answer 3

I guess it's hard for you to understand. maybe i will present my answer to you tomorrow.

Answer 4

Wow, that sure is a way to find it. But it is a short answer question and you should spend max 6 minutes on it. :/ Well, I'm starting to think you have to use calculator for this one. But thanks anyways :)

Answer 5

No, I understand what you mean :)

Answer 6

another way I thought of would be combining sin 3x and sin 6x into 2sin cos form. But i don't think we can draw the graph from there. might still need the same method to draw. If you understand then I can save my time doing this question. XD

Answer 7

Yeah, you put a lot of effort already and I appreciate it :)
Thanks again.