Help with Trigonometry: Solving sinx + sin(x/2) = 0

In summary, to solve for x in the equation sinx + sin(x/2) = 0, you can use the double angle identity for sine and then substitute u = sin(x) to solve for u. You can also use a calculator to solve this equation, but make sure it is set to radians mode. There are multiple solutions for this equation, and knowing the double angle identity for sine and the half angle identities for sine and cosine can be helpful in solving it.
  • #1
CathyLou
173
1
Hi.

Could someone please help me with the following question? I would really appreciate any help as I am completely stuck at the moment.

Solve sinx + sin(x/2) = 0 when x is between (and including) 0 and 360 degrees.

Thank you.

Cathy
 
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  • #2
Hey Cathy,

Try writing;

[tex]\sin(x) = -\sin(x/2)[/tex]

[tex]\sin(x) = \sin(-x/2)[/tex]
 

1. How do I solve for x in the equation sinx + sin(x/2) = 0?

To solve for x in this equation, you can use the double angle identity for sine: sin(2x) = 2sin(x)cos(x). Rearrange the equation to get sin(2x) = -sin(x). Then, substitute u = sin(x) to get sin(2x) = -u. This can be solved by finding the solutions for u and then substituting back in for x.

2. What are the key steps in solving this trigonometry equation?

The key steps in solving this equation are: 1) using the double angle identity for sine, 2) substituting u = sin(x), 3) solving for u, and 4) substituting back in for x to find the final solutions.

3. Can I use a calculator to solve this equation?

Yes, you can use a calculator to solve this equation. However, make sure your calculator is set to radians mode since the solutions will be in radians.

4. Are there any special angles or identities I should know for solving this equation?

Yes, there are a few special angles and identities that can be helpful in solving this equation. These include the double angle identity for sine, as well as the half angle identities for sine and cosine.

5. Is there more than one solution for this equation?

Yes, there are typically multiple solutions for this type of equation. The number of solutions will depend on the value of the coefficient in front of x (in this case, 2).

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