# How to Graph Trig Functions

1. Jan 7, 2009

### 312213

1. The problem statement, all variables and given/known data
How do I input trig functions in the calculator?
An example would be cos(2t) = 0.5.

2. Relevant equations

3. The attempt at a solution
I don't understand how to start it.
How do I input this in? I am not sure how to input it into a graphing calculator. The equation to input it into y = ? would be greatly appreciated.

2. Jan 7, 2009

### Thaakisfox

What you want to do is solve the equation. So for that you need, some program which solves the equation, and which most probably the calculator doesnt have. If you simply want to graph the function then input: y=cos(2t) .

3. Jan 7, 2009

### 312213

The 0.5 is what I am trying to find. I forgot that's what it means. So the 0.5 would actually be at what t would I get 0.5.

Thanks for clearing that up for me.

4. Jan 7, 2009

### Dick

If cos(2t)=0.5 then 2t=arccos(0.5). arccos (or cos^(-1)) is the inverse cosine function. Is it on your calculator? Once you have that, you know that that's not the only solution. Draw a graph of cos. There are many solutions, the arccos will only give you one. In this case though, you don't even need the calculator. There is a simple triangle you can draw with an angle in it that has a cos of 1/2.

5. Jan 7, 2009

### 312213

The first angle would be 30°, or $$\pi$$/6.

If say I am to find the radians that equal 0.5 for functions 0 $$\leq$$ t $$\leq$$ 2$$\pi$$, then the first one is $$\pi$$/6. The rest of them are found by subtracting $$\pi$$ - $$\pi$$/6 = 5$$\pi$$/6, adding $$\pi$$ + $$\pi$$/6 = 7$$\pi$$/6, and subtracting 2$$\pi$$ - $$\pi$$/6 = 11$$\pi$$/6.

This means that there and four answers and they are $$\pi$$/6, 5$$\pi$$/6, 7$$\pi$$/6, and 11$$\pi$$/6.

Is this correct?

Edit: Something small and not important but is there a way to have the pi sign not look like exponents using the forum's posting ability options and not resorting to copy/pasting character map's pi? Which still looks pretty bad. π

Last edited: Jan 7, 2009
6. Jan 7, 2009

### jgens

Just a brief note. If your calculator can find intersections between curves you could graph the two functions y = cos(2t) and y = 0.5 and find any intersections.

7. Jan 7, 2009

### Dick

Yes, I think. Try $$\frac{\pi}{6}$$. Click on the symbol to see how it works.

8. Jan 12, 2009

Yep, looks right to me dude

9. Jan 13, 2009

### HallsofIvy

Staff Emeritus
Put entire expressions, not just individual symbols, in LaTex.

$$\frac{\pi}{6}$$
or
$$\pi/6$$

Instead of $$\pi$$/6