Draw f(x)=3sinx+cosx

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Leah5467

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Feb 28, 2019
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Hi my question is this:
maths.png
i don't know how to begin with. I know the answer but don't know the process...
Thank you!
 
Leah5467 said:
Hi my question is this:
View attachment 12329
i don't know how to begin with. I know the answer but don't know the process...
Thank you!
Click to expand...
12331
f(x) = 3 * Sin(x) + 4 * Cos(x)

f(x) = √(32 + 42) * [3/5 * Sin(x) + 4/5 * Cos(x)]

Let

Sin(Φ) = 4/5 ........... and Cos(Φ) = 3/5 → Φ = Sin-1(4/5)

Then

f(x) = 5 * [3/5 * Sin(x) + 4/5 * Cos(x)] = 5 * Sin (x + Φ)

continue....

Alternatively, you could make a chart of f(x) at different values of 'x' and plot that.
 
Thank you! But i don't really get what this part:f(x) = √(32 + 42) * [3/5 * Sin(x) + 4/5 * Cos(x)] is doing.
 
Leah5467 said:
Thank you! But i don't really get what this part:f(x) = √(32 + 42) * [3/5 * Sin(x) + 4/5 * Cos(x)] is doing.
Click to expand...
I am multiplying and dividing f(x), by √(32 + 42)

If you are not familiar with this method - go the alternative way - make a chart of f(x) at different x's and plot it.
 
So is it possible to do it without a calculator for plotting different x? Is it expected for a year 12 student to do it? I am worried that it is a question that is on the non-calc test.
 
Leah5467 said:
So is it possible to do it without a calculator for plotting different x? Is it expected for a year 12 student to do it? I am worried that it is a question that is on the non-calc test.
Click to expand...
It will be a bit difficult (knowing values of √3 and √2 etc.) and time consuming - but possible.

I did it in my high school days when hand-held calculators were called abacus.
 
Ahh i see. I suppose abacus is a lot more time-consuming ? and if they still let you guys do it with an abacus,i think that we have to do it as well. How about the alternative method? Which topic is it related to?
 
I think the only thing you would need a calculator for is to find Φ = Sin-1(4/5) . Are you saying you not only can't use a graphing calculator, but can't calculate trig functions at all? Then I suppose you would be expected to estimate roughly. Note that it only says to sketch the graph.

What are the exact instructions for this problem, and for calculator usage on the test?

The basic method Khan showed is standard, using the angle-addition identity, allowing you to identify peaks and other features. The next-easiest method would probably be calculus. Plotting individual points would require more use of the calculator.
 
I don't know the rules for calculator usage on this test ?I don't understand the not using plotting graph method though...so welp?I guess i have to go by the other method,hopefully it is on calculator test.
 
With no calculator, I'd just estimate Φ = Sin-1(4/5) as about 60 degrees and do the sketch. Or you might have seen that angle enough to recall that it's closer to 53 degrees.
 
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