# sin(pi-x) Formula | Formula of sin(pi-theta)

For any x, sin(pi-x) formula is given below:

sin(pi-x)=sinx

Similarly, sin(pi-theta)=sin theta. In this post, we will learn how to compute sin(pi-x) or sin(pi-theta).

## sin(pi-x) Simplify

To find the formula of sin(π-x), we will apply the following trigonometric identity:

sin(A-B) = sinA cosB – cosA sinB …(∗)

Here we put A=π and B=x; so that we get

Thus we have established the formula of sin(π-x) which is given by

Note: In a similar way, we obtain the formula of sin(π-θ) which is given by sin(π-θ) = sinθ.

More Readings: How to Simplify cos(π-x)

Values of sin15, cos 15, tan15

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## Simplify sin(x-pi)

The formula of sin(x-π) is given by

sin(x-π) = -sinx.

To prove it, we will put A=x, B=π in (*). Thus, we obtain that

Hence, we obtain the formula of sin(x-π) which is equal to sin(x-π) = -sinx.

Question: Find the value of sin(-150°)

We have sin(-150°) = sin(30°-180°)

So sin(-150°) = sin(30°-π)

⇒ sin(-150°) = -sin30° using the above formula sin(x-π) = -sinx with x=30°.

⇒ sin(-150°) = -1/2 as the value of sin30 is 1/2.

So the value of sin negative 150 is equal to 1/2

How to simplify cos(sin-1x)

## FAQs

Q1: What is the Formula of sin(π-x)?

Answer: The formula of sin(π-x) is given by sin(π-x)=sinx.

Q2: What is the Formula of sin(x-π)?

Answer: The formula of sin(x-π) is given by sin(x-π)=-sinx.