# How do I solve sin x x

## Solve sine equations of the form sin (b x + c) + d = 0

Let's look at the zeros and note that we don't change the zeros when we stretch or compress the graph:

~ plot ~ sin (x); 2 * sin (x); 5 * sin (x); hide ~ plot ~

However, if we add up a value, all zeros change:

~ plot ~ sin (x) +0.5; 2 * sin (x) +0.5; 5 * sin (x) +0.5; 0.5; hide ~ plot ~

Each zero or each point of the zero shifts upwards.

### Solution formula for zeros of sin (b x + c) + d = 0

Taking d into account, the following general solution formula for zeros can be derived:

Let's do another sample exercise to be more secure:

Solution formula:

Let's check the solution graphically:

~ plot ~ sin (2x + 30/180 * pi) -0.5; x = 0; hide ~ plot ~

We see the zero at.

If we need the solutions in the case of an unbounded interval, we still have to determine the period.

period
period

The zero formula is thus:

Let's draw the graph and see if we can find the zero again:

The first zero is at, another at. But there is also a second zero, how do we calculate this? To do this, we again use the identities:

However, our term is not x, but rather. We now have to use this for the identity formula:

Let's reshape that:

And let's now insert the zero.

Now we need to determine the x value that leads to.

The second zero is therefore at 60 °. Here, too, we define the period totals:

period
period

The solutions for the zeros summarized:

Tip: The program Zeroing for sine functions helps to check the correctness of the solutions that have been determined for various tasks.