How important is sketching trig functions? (1 Viewer)

[enigma_1]

Like how do you sketch y= 1 + sin (pi/2)x ?

These are too hard for me

Is it sufficient knowing the basic ones where only the amplitude and period vary?

regards

 

[Carrotsticks]

Unfortunately that is not enough. You need to be able to sketch trig functions in the form y= Asin(kx+B)+C or same for cos and tan.

Something like that can have up to 5 transformations on the original function. Usually in the HSC, they ask for 1 or 2 transformations (ie: Shifted down by 3, amplitude magnified by 2).

 

[emilios]

Hey mate, usually trig function graphs are the easy ones you mentioned such as Asin(nx) and they tend to appear in earlier questions. However, it is essential that you know how to do transformations.

For something in the form of sin(nx), the period is given by 2pi/n. In this case, 'n' is pi/2. So the period is 2pi / (pi/2) = 4 (i.e. the sine curve has completed a full oscillation/cycle at x=4).

The next part (the +1) involves moving the whole curve up 1 unit. Anytime you add a constant to a curve, it moves either up or down the y axis by that many units. It helps if you first sketch y=sin (pi/2)x first on a bit of working out paper in a test, then copy the entire graph but moved up one unit on your answer paper (in this case, all the zeroes would be on the line y=1 instead).

 

[enigma_1]

Ohh okay thanks guys!! I will try and perfect my trig graphs. Some textbooks don't give you the full rules so I'll have to research it. Also, can you guys help me with how to find the amplitude of y=cosx + sinx ? Approximate answer is 1.4 but I don't get how to actually find it.

 

[Carrotsticks]

Ohh okay thanks guys!! I will try and perfect my trig graphs. Some textbooks don't give you the full rules so I'll have to research it. Also, can you guys help me with how to find the amplitude of y=cosx + sinx ? Approximate answer is 1.4 but I don't get how to actually find it.

There are 2 ways.

- Auxiliary Angle method, turning that function into root(2) * sin(x+pi/4) (3U topic)

- Using differentiation to find the stationary points and showing that the max/min is y=root(2).

 

[enigma_1]

There are 2 ways.

- Auxiliary Angle method, turning that function into root(2) * sin(x+pi/4) (3U topic)

- Using differentiation to find the stationary points and showing that the max/min is y=root(2).

Ok, for the auxiliary angle thing you need sinx+cosx to equal something right? How do you do it without it?

 

[enigma_1]

Sorry sorry, can someone help me with this one? y=3sin2x - 4cos2x ? How to get the amplitude for this one? The auxiliary angle thing wont work cause it's a double angle am I correct>??

 

[Carrotsticks]

Ok, for the auxiliary angle thing you need sinx+cosx to equal something right? How do you do it without it?

Yep that's the one, you let it equal Rsin(x+a)

Without using that, you have to use trig calculus. Let y=sin(x)+cos(x), differentiate and let it equal zero etc etc.

However, there's a chance that since the answer provided was an approximation, you were expected to sketch y=sin(x), y=cos(x) and then add the two functions.

Sorry sorry, can someone help me with this one? y=3sin2x - 4cos2x ? How to get the amplitude for this one? The auxiliary angle thing wont work cause it's a double angle am I correct>??

It still works, you just have to equate it with Rsin(2x+a).

Due to the nature of the coefficients (3 and 4 will result in an R value of 5), this leads me to believe that the question intended for you to use the R method.

Generally they pick the coefficients such that you get a nice value of R.

 

[enigma_1]

Yep that's the one, you let it equal Rsin(x+a)

Without using that, you have to use trig calculus. Let y=sin(x)+cos(x), differentiate and let it equal zero etc etc.

However, there's a chance that since the answer provided was an approximation, you were expected to sketch y=sin(x), y=cos(x) and then add the two functions.



It still works, you just have to equate it with Rsin(2x+a).

Due to the nature of the coefficients (3 and 4 will result in an R value of 5), this leads me to believe that the question intended for you to use the R method.

Generally they pick the coefficients such that you get a nice value of R.

Wow thank you soo much!! This is very helpful

 

[emilios]

Just note that in a 2U paper, they're probably expecting you to differentiate the function to find the amplitude (coz the amplitude is the max value). Its also good to keep in mind if you have ugly or mismatched angles that you can't use the auxiliary angle method on.

 

[hit patel]

Yes. The easier way by algebra is to remeber the domain of the function and instead of the original x value sub in the value provided instead. i.e. instead of sin (x) if provided sin(2x + pi) the let -pi/2 < 2x + pi < pi/2 to find domain and to find range sub in the values of domain found into the original function. Easy method? You can use this same methodd for inverse functions except as the name suggest the x and y values will interchange and therefore domain wont be a radian and range will be.

 

[hit patel]

Just note that in a 2U paper, they're probably expecting you to differentiate the function to find the amplitude (coz the amplitude is the max value). Its also good to keep in mind if you have ugly or mismatched angles that you can't use the auxiliary angle method on.

Differentiate? with this they ask you to find this to see the gradient at the point so you can determine whether a sharp point or vertical tangent? And amplitude is the coefficient already before the trig function