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

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


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) Formula

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

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

⇒ sin(π-x) = 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.

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

Values of sin15, cos 15, tan15

General Solution of tanx=tany

General Solution of sinx=1 | General Solution of sinx=-1

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

⇒ sin(x-π = sinx⋅ (-1) – cosx ⋅ 0

⇒ sin(x-π = -sinx.

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

Question Answer

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

Also Read:

How to simplify cos(sin-1x)

1-sec2x Formula | 1+cot2x Formula


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.

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