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## #1 2006-05-31 04:01:07

yonski
Member
Registered: 2005-12-14
Posts: 67

### Solving an equation?

If i'm told that 0 = -2sin(0.5x) + cos(0.5x) , how would i go about finding x in this situation? Is this called a trigonometric equation, i'm not sure?

Thanks.

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Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

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## #2 2006-05-31 05:12:07

numen
Member
Registered: 2006-05-03
Posts: 115

### Re: Solving an equation?

Yes, it's a trigonometric equation.

try using this identity:

Where C is

for A<0. If A would be bigger than 0 (not in this case!), then you'd just skip π (pi).

Divide so you only get sin(x+C) on one side. From there you can get (x+C) alone on one side, and thus solving for x.

There are plenty of trigonometry formulas over here: http://www.mathsisfun.com/forum/viewtopic.php?id=3290

Hope this helps, I haven't solved any trigonometry equation in ages, anyone else wanna do the math?

Last edited by numen (2006-05-31 05:16:46)

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## #3 2006-05-31 09:01:38

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Solving an equation?

yonski wrote:

If i'm told that 0 = -2sin(0.5x) + cos(0.5x) , how would i go about finding x in this situation? Is this called a trigonometric equation, i'm not sure?

Thanks.

well i would solve it this way

tangent repeats every 180degrees, so if you wanted the possible values of x between -360 and 360 degrees, we would have

x = 53.13010235...
x = -306.8698976...

which if you plug back into original equation, equals 0

Last edited by luca-deltodesco (2006-05-31 09:09:43)

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## #4 2006-05-31 09:12:19

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Solving an equation?

2*arctan(1/2) and then you can add or subtract 2*pi to that as many times as you want for more answers.
If it wasn't 2x in the cos and sin, but was just x, then you'd get answers in first and third quadrants and you would have been able to add just pi or subtract pi.

You still can think of it that way except adding pi is to x/2, so if you get rid of the 1/2, you add 2*pi to x, effectively.

The reason I used the arctan is because the equation you gave essentially said that sine or height is 1/2 of
the width or cosine, hence rise/run is 1/2, which is the tangent of the angle.

The reason you are allowed to reason it out is because the frequency or wavelength of the sine and cosine functions are identical.   If one was sin(x/3) and the other was cos(x/2), then it would be harder for sure!

So 53.13 degrees is one answer for x, and add 360 or subtract 360 etc.

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