Trigonometry/Identities
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(Redirected from Lesson 3:Trigonometric Identities)
Let us take a right angled triangle with hypotenuse length 1. If we mark one of the acute angles as , then using the definition of the sine ratio, we have
As the hypotenuse is 1,
Repeating the same process using the definition of the cosine ratio, we have
Pythagorean identities
[edit | edit source]Since this is a right triangle, we can use the Pythagorean Theorem:
This is the most fundamental identity in trigonometry.
From this identity, if we divide through by squared cosine, we are left with:
If instead we divide the original identity by squared sine, we are left with:
There are basically 3 main trigonometric identities. The proofs come directly from the definitions of these functions and the application of the Pythagorean theorem:
Angle sum-difference identities
[edit | edit source]Cofunction identities
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