Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x)

in MES Science19 days ago (edited)

In this video I show some very useful trigonometric identities which basically involve shifting the sine or cosine functions by either 2π or 360 degrees and π/2 or 90 degrees. Make sure you understand these and keep them in mind because I will use these many times in later videos.

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Trigonometry Identities

Trig Identities - sin(2pi + x) Resized AI.jpeg

cos(2π + ϴ) = cos(ϴ) and sin(2π + ϴ) = sin(ϴ)

Adding 2π is the same as adding 360°; which means we can just rotate the angle by a full revolution until it gets back to the same line. The ratios stay the same so the identity becomes itself!


cos(π/2 - ϴ) = sin(ϴ) and sin(π/2 - ϴ) = cos(ϴ)

Subtracting an angle from π/2 is the same as subtracting it from 90°; which means the resulting ratios get flipped as per the image below.


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