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