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

sin(π-x) = sinπ cosx – cosπ sinx

= 0⋅cosx – (-1) sinx as we know that sinπ=0 and cosπ=-1.

= sinx.

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

sin(π-x) = sinx |

In a similar way, we obtain the formula of sin(π-θ) which is given as follows:

sin(π-θ) = sinθ |

## 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

sin(x-π) = sinx cosπ – cosx sinπ

= sinx⋅ (-1) – cosx ⋅ 0

= -sinx.

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

**Also Read:**

## 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.