rachelmaddie
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- Aug 30, 2019
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Hi. I wanted to check if this was the proper way to verify a identity for my precalc class.
The given identity, sin θ = sin (180 - θ), is true based upon a proven identity: sin (θ ‒ Ф), the “Difference of Two Angles” formula:
sin (θ ‒ Ф) = sin Ѳ cos Ф ‒ cos Ѳ sin Ф .
Using the “Difference of Two Angles” formula, we can manipulate the right side of the given equation as follows:
sin (180° ‒ Ѳ) = sin 180° cos Ѳ ‒ cos 180° sin Ѳ
= (0) cos Ѳ ‒ (‒1) sin Ѳ
= 0 ‒ (‒ sin Ѳ)
= (‒1)(‒ sin Ѳ)
= sin Ѳ
The given identity, sin θ = sin (180 - θ), is true based upon a proven identity: sin (θ ‒ Ф), the “Difference of Two Angles” formula:
sin (θ ‒ Ф) = sin Ѳ cos Ф ‒ cos Ѳ sin Ф .
Using the “Difference of Two Angles” formula, we can manipulate the right side of the given equation as follows:
sin (180° ‒ Ѳ) = sin 180° cos Ѳ ‒ cos 180° sin Ѳ
= (0) cos Ѳ ‒ (‒1) sin Ѳ
= 0 ‒ (‒ sin Ѳ)
= (‒1)(‒ sin Ѳ)
= sin Ѳ
