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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Cos minus theta equals cos theta
Question-Answer
| Question: Find the value of sin(-30°). |
Answer:
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
FAQs
Q1: What is sin minus theta?
Answer: Sin minus theta equals minus sin theta, that is, sin(-θ) = -sinθ.