Istock: Roller Coaster

“What goes up must come down”

“Life is full of ups and downs”

“Life is a roller – coaster”

“Happiness is an interval between two pains”

Istock: Riding on a roller coaster

Graph drawn using: Desmos

__What is a Sine Curve?__

The x-axis on the sine curve plots time, the y-axis plots how we feel. The higher the points on the y-axis, the greater the happiness. In other words, the greater the amplitude of the curve at any particular point in time, the greater the amount of happiness at that particular time. For this discussion, we assume that y=0 be the point in our lives where we feel neutral (neither happy nor sad).

__Accuracy of the Sine Curve:__

It is certainly not accurate to use the sine curve to draw parallels to the ups and downs of life. Hear me out….

Firstly, the period of happiness in certain times of our lives may be longer than those of depression (hopefully). That is to say, the curve above the y-axis may spread over a longer period (of time) than the curve under the y-axis. This, you may argue, may also happen when the period of grief is longer than the period of happiness.

Another problem we may face is the question on how we measure happiness. How do one measure the difference in happiness between receiving news of a great promotion to getting a new car? This shows that the amplitude of happiness will or may always differ and it would be subjective from person to person.

How then is the sine curve relevant? Indeed, if you look at life as a whole, or sometimes, simply mood in a day and try to chart it, it may somewhat resemble a sine curve. Perhaps you felt tired in the morning (starting with below y =0) but your child came in and showed you a beautiful drawing of hers. Or in another incident, perhaps you were looking forward to meeting your date only to realise that he/she has cancelled it at the last minute.

These may be extreme cases to you or perhaps your sine curve may not peak at a level that you might expect. I certainly hope that your trough would not be as low as you would expect.

__What do we learn about life from the sine curve?__

By its very nature, the sine curve demonstrates that very little in life happens in straight lines and that we all go through peaks and troughs, highs and lows as part of our life’s journey.

By now you must be wondering what the blue line y = 0.5 represents. Well, it may be a hypothetical situation; some call it ‘bliss’ or ‘achieving equanimity’. In a case like this, one’s mood is constant or close to the same, regardless of their surroundings and not affected by different situations. If you have any idea on how to achieve that, write in the comments below!

For most of us, we probably need to recognise that wherever we are on the sine curve at this particular point in our life; we must appreciate and enjoy the highs. When we are feeling low or lost, don’t give up yet, somewhere, someday, things will get high once again!

__For other discussion:__

You may also use the Cosine curve to explain. Afterall, the Cosine curve is a sine curve shifted to the left by 90 **° **or** **(Pi/2)

For more reading:

For drawings:

__https://www.desmos.com/calculator__

For Sine curve:

__https://www.youtube.com/watch?v=e1kZwzxOFUQ__

#trigonometry #sine #cosine #geometry #life #application #reallifemath