Can I Sketch the Graph of \sin\Theta = \frac{\pi}{2} - \Theta Symmetrically?

[Tau]

This is the problem:

Sketch the graph of:

$$\sin\Theta$$ = $$\frac{\pi}{2}$$ - $$\Theta$$


Now the graph (between 0 and pi) is symmetrical about the line

$$\Theta$$ = $$\frac{\pi}{2}$$

So I can write the equation as

$$\sin\Theta$$ = $$\frac{\pi}{2}$$ + $$\Theta$$

This will be a graph of $$\sin\Theta$$ pulled $$\frac{\pi}{2}$$ units to the left.

Is this reasoning correct?

If it is, would you do it a different way?


Thanks
Jeremy

(Noone wants a gmail invite?lol!)

 

[laker88116]

What I am not understanding is how you sketch it on a coordinate plane if there is only one variable (theta).

 

[Tau]

I am SUCH AN IDIOT!

I mistyped the entire question. You all now see what a dufus I am.

Anyway, here is the question (typed properly this time):

Sketch the graph of:

y = $$\sin(\frac{\pi}{2}$$ - $$\Theta$$)

and using the same reasoning above I end up with

y = $$\sin(\Theta$$ + $$\frac{\pi}{2}$$)

Which is a curve of $$sin\Theta$$ pulled half pi units to the left
Now- is this reasoning correct.

If it is, would any of you done it a different way?

 

[gaganpreetsingh]

Both of the expressions are equal to cos theta.

 

[Tau]

I know that both curves are the same.

But I want to know if I reasoned it out correctly.

Were the actions I took (see first post) the correct ones. Was I thinking along the correct lines?

 

[Tau]

I can see that no one is interested in giving me an answer.

Oh well.

 

[AKG]

Yes, your reasoning is fine.

 

[Renge Ishyo]

Well, both equations do simplify to cos theta, so yeah they are the same function. If you meant, "how do I see for sure that they are the same function?" you can always try substitution.

sin theta when theta equals zero is zero. Substituting (using degrees because I don't have those pretty graphics), your first equation becomes:

y = sin (90 - 0) = sin (90) - sin (0) = 1 - 0 = 1

Then your next equation becomes:

y = sin (0 + 90) = sin (0) + sin (90) = 0 + 1 = 1

To check to see that both equations can be substituted for simply y = cos (theta).

y = cos (0) = 1

The math police would probably arrest me if they found me dumping in numbers like this when you are probably asking for a formal proof, but it's good enough for me so I hope it helped.

 

[Tau]

Thanks guys

I thought for a moment that I was alone in the dark.

More questions to come soon!