# Homework Help: Trig Equation

1. Oct 3, 2005

### cscott

3 cos x + 4 = 0
cos x = -4/3

How do I solve this? I can't take the arcsine...

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sin (3x - 40) = 0

Is the general solution 73.3 + 120k | k E I?

2. Oct 3, 2005

### robphy

Did you try to use complex numbers or hyperbolic trig functions?

3. Oct 3, 2005

### hotvette

Could try graphing it and see where it crosses zero.

4. Oct 3, 2005

### Jameson

It's not going to cross the x-axis. You'll have to encorporte complex numbers like robphy said.

5. Oct 3, 2005

### cscott

We don't cover complex numbers until the end of the year. Does this mean I say it has no solution?

6. Oct 3, 2005

### JoshHolloway

Why can you not take the cosine inverse of x?

7. Oct 3, 2005

### cscott

4/3 > 1 so you get a domain error... or at least that's how I see it.

8. Oct 3, 2005

### benjamincarson

Unless I'm missing something, your given value for cos x is incorrect. Any value of the cosine function is in a way "stuck" between -1 and 1.

Use a calculator and take the cosine of any degree/radian measure you wish, it will always be between -1 and 1.

Last edited: Oct 4, 2005
9. Oct 3, 2005

### cscott

I got -4/3 from rearranging the equation. The fact that 4/3 > 1 is my problem.

10. Oct 3, 2005

### benjamincarson

Is this an equation that needs solving, or an identity that needs verifying?

11. Oct 3, 2005

### cscott

"Solve for all possible values of x."

12. Oct 3, 2005

### benjamincarson

no solution

13. Oct 3, 2005

### cscott

Thank you.

14. Oct 4, 2005

### cscott

I have another problem

sin^2 x = 3/4

for one of the possible answers I get $\frac{\pi}{3} + 2\pi k$ but my book says it should be $\pi$ instead of $2\pi$ for the period. How come?

15. Oct 4, 2005

### whozum

The sin value is squared, so the negative values square out to give a solution too.

16. Oct 4, 2005

### cscott

Yes I know. Let me clarify: $\frac{\pi}{3} + 2\pi k$ is one possible solution but my book says it should be $\frac{\pi}{3} + \pi k$ and I don't know why.

17. Oct 4, 2005

### robphy

$$e^{i\pi}=-1$$

18. Oct 4, 2005

### cscott

I haven't done complex numbers so I don't really know the significance of that expression.

19. Oct 4, 2005

### TD

$$\sin ^2 x = \frac{3} {4} \Leftrightarrow \sin x = \pm \sqrt {\frac{3} {4}} = \pm \frac{{\sqrt 3 }} {2}$$

Now determine the solution in both cases (the + and the - case).

20. Oct 4, 2005

### cscott

I would say

$$\frac{\pi}{3} + 2\pi k | k \epsilon I, \frac{4\pi}{3} + 2\pi k | k \epsilon I$$

but my book says

$$\frac{\pi}{3} + \pi k | k \epsilon I, \frac{4\pi}{3} + \pi k | k \epsilon I$$

and I don't know why