Trigonometry

[Leah5467]

Hi my question is b:


i don't really get how to draw or where to start with.
Thank you!

 

[Dr.Peterson]

Surely you know how to plot y = 1 + cos(x)! Just find the key points in one cycle of the graph, and plot them. I don't think there is any trick intended.

Now, if you had shown the entire problem, as we request, we might know what form they gave for f(x), and there might be something more interesting to say. I imagine there is some specific point to the problem, but you have hidden it.

The attachment seems utterly unrelated.

 

[Leah5467]

Thank you! The part missing is f(x)=1+sin2x
i don't understand how to find the key points of 1+cosx. I don't know which is the maximum point if f(x)=1+2sinx.
I uploaded the wrong attachment and i forgot to delete it ?

 

[Dr.Peterson]

Thank you! The part missing is f(x)=1+sin2x

That makes no sense. If they defined f as f(x) = 1 + sin(2x), then why would part (a) say, "Show that f(x) can be expressed as 1 + sin(2x)"???

i don't understand how to find the key points of 1+cosx. I don't know which is the maximum point if f(x)=1+2sinx.

IGNORE f(x)! It doesn't say anything about using f to graph g.

Where is the maximum of 1 + cos(x)? When x = 0 or 2 pi, right?

Now, when you show us the entire problem, I'll be able to say something about how the parts are related -- if they are.

 

[Otis]

... i don't understand how to find the key points of 1+cosx ...

Hello. Can you see that 1 is added to the y-coordinate of every point on the graph of y=cos(x)? In other words, the graph of y=cos(x)+1 is the graph of cosine shifted vertically upward one unit.

By the way, cosine and sine are functions, so I think we ought to use function notation: cos(x) and sin(x). Cheers

?

 

[Harry_the_cat]

When asked to graph the function y =f(x), we can find key points such as axes intercepts, stationary points (using calculus), asymptotes, and what happens at the extremes.
When asked to graph a trig function though, as in your question, there is no need to do this. Trig functions in the form y = a sin(b(x-c)) + d or y = a cos (b(x-c)) + d are best graphed by identifying a, b, c and d and interpreting their effect on the basic sin or cos graph.

Have you learnt about transforming trig functions?