Trig y=sinx-sin x/2 ? (1 Viewer)

[Fiction]

How would you solve/graph for questions such as y= sinx - sinx/2? I get how to draw y = sinx and y = sinx/2 but I'm stumped with a question that combines the two. (other examples are y = 2cos x + 3sinx etc)

If anyone could explain, I'll really appreciate it<3

 

[Drsoccerball]

How would you solve/graph for questions such as y= sinx - sinx/2? I get how to draw y = sinx and y = sinx/2 but I'm stumped with a question that combines the two. (other examples are y = 2cos x + 3sinx etc)

If anyone could explain, I'll really appreciate it<3

It depends on the difficulty of maths you're doing. If youre not doing extension 1 or higher you wouldnt be able to solve this

 

[Drsoccerball]

But just in case you are interested one way is drawing the graphs separately and adding the y coordinates.
Or the more longer way and just use differentiation and table of values..

 

[Fiction]

It depends on the difficulty of maths you're doing. If youre not doing extension 1 or higher you wouldnt be able to solve this

This is for 2u homework so I'm hoping this can be solved lol. An explanation geared towards a 2u maths student would be great

Thanks in advance to anyone who'll help )

 

[Ekman]

How would you solve/graph for questions such as y= sinx - sinx/2? I get how to draw y = sinx and y = sinx/2 but I'm stumped with a question that combines the two. (other examples are y = 2cos x + 3sinx etc)

If anyone could explain, I'll really appreciate it<3

Ok so you sketch both y=sinx and y=sinx/2 (basic 2u knowledge), then you subtract the y values of each point. For example, at x=pi/2 you would do 1-1/root2 (since sinpi/2 = 1 and sinpi/2/2 =sinpi/4 = 1/root2 ) Thus you just do this over a domain of x values for example 0 to 2pi.

 

[Fiction]

But just in case you are interested one way is drawing the graphs separately and adding the y coordinates.
Or the more longer way and just use differentiation and table of values..

Hum, I'm not sure if this is waht you meant but for y = 2cos x + 3sinx I drew the two graphs then figured out what Y is by getting a line which lies in between the previous two. I don't know how right that is though haha. I was wondering, the method I just mentioned be legit, then what's the difference between a y = 2cos x + 2sinx and y = 2 cosx - 2 sinx. So what does a change in sign entail?

 

[Squar3root]

This is for 2u homework so I'm hoping this can be solved lol. An explanation geared towards a 2u maths student would be great

Thanks in advance to anyone who'll help )

draw sin(x) and sin(x/2) and subtract the y values of sin(x/2) from sin(x)

 

[Ekman]

Plus year 11 physics covers this as well, in the waves chapter...

 

[Ekman]

Hum, I'm not sure if this is waht you meant but for y = 2cos x + 3sinx I drew the two graphs then figured out what Y is by getting a line which lies in between the previous two. I don't know how right that is though haha. I was wondering, the method I just mentioned be legit, then what's the difference between a y = 2cos x + 2sinx and y = 2 cosx - 2 sinx. So what does a change in sign entail?

The change in sign means that either if its +, the y values of 2cosx and 2sinx will add, or when its -, the y values of 2cosx and 2sinx will minus each other

 

[Ekman]

Plus why would you need to sketch two trig graphs together in 2u, I remember doing it in extension 1. In 2u all I remember is how trig graphs are differentiated and integrated, that's it!

 

[Drsoccerball]

True ekman and i never did sketching of graphs like the ones you speak of in two unit. In extension 1 we were sketching graphs with sin and cos and in extension 2 we sketched by adding y values...You wont be asked in the hsc to sketch such graphs as extension 1 students will have an advantage.

 

[braintic]

True ekman and i never did sketching of graphs like the ones you speak of in two unit. In extension 1 we were sketching graphs with sin and cos and in extension 2 we sketched by adding y values...You wont be asked in the hsc to sketch such graphs as extension 1 students will have an advantage.

Using calculus, it it perfectly legitimate in 2U to ask for the turning points of functions which are linear combinations of sin and cos.
The resulting equation for finding turning pts is a simple tanx = c.

In the 1998 2U HSC, whilst they didn't ask for a sketch, they asked for the max and min values of y=1+(√3)sinx + cos x.
That is something that would definitely advantage Ext 1 students ... they could basically write the answers straight down.