Is square root 1 minus cosine squared theta = −sin Θ true? If so, in which quadrants does angle Θ terminate?

The trigonometric identity states that the sum of the square of cosine and sin is equal to 1. In this case, the identity is tried to rearrange and tried to verify if the statement above is true.

Square root 1 minus cosine squared theta = −sin Θ
This is only true in angles tried such as (360-45) or (270-45). hence Θ should be in quadrant III and IV only

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azikennamdi azikennamdi · Answer 2 · 2022-05-18T11:47:51+02:00

The quadrants in which angle Θ terminates is given as: Quadrant 3 and 4 only. That is Q3 and Q4.

What is a Quadrant?

In mathematics, a quadrant refers to an area or a space that houses the two traditional axes - X and Y.

To show the position of the quadrants, we say:

√(1-cos² θ) ≥ 0. Note that this is also equals

√(1-cos² θ) = sin θ (In absolute form).

Hence, the above is equal to sin θ if θ ∈ Q1 or Q2. It also means that

= - sin θ, if θ ∈ Q3 or Q3

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