Sin(-theta) equals -sin theta: Proof | Sin minus theta

Sin minus theta is equal to minus sin theta, that is, sin(-θ) = -sinθ. Here we will learn how to find the value of sin of minus theta.

The sin minus x formula is given by sin(-x) = -sinx.

Prove that sin(-theta) = -sin theta

To compute sin(-theta), let us follow the below steps. The steps are

Step 1:

At first, we write -θ = 0-θ

Step 2:

Thus, we have that

sin(-θ) = sin(0-θ)

= sin0 cosθ – cos0 sinθ, by the formula sin(a-b) = sina cosb – cosa sinb with a=0 and b=θ

= 0 × cosθ – 1 × sinθ, as the values of cos0 and sin0 are 1 and 0 respectively.

= 0 – sinθ

= -sinθ.

In other words, sin(-θ) = -sinθ.

Therefore, the value of sin(-θ) is equal to -sinθ.

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Question: Find the value of sin(-30°).


In the above formula of sin(-θ) = -sinθ, we put θ=30°. So, we have that

sin(-30°) = -sin30° = -1/2.

So the value of sin -30 degree is equal to -1/2.

Also Read: sin(x+y+z) formula, proof

cos(x+y+z) Formula | tan(x+y+z) formula


Q1: What is sin minus theta?

Answer: Sin minus theta equals minus sin theta, that is, sin(-θ) = -sinθ.

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