Identities are equations true for any value of the variable.
Since a right triangle drawn in the unit circle has a hypotenuse of length 1, we define the trigonometric identities x = cos(theta) and y = sin(theta).
In the same triangle, tan(theta)=x/y, so substituting we get tan(theta) = sin(theta)/cos(theta), the tangent identity.
Another key trigonometric identity sin2
(theta) + cos2
(theta) = 1 comes from using the unit circle and the Pythagorean Theorem.
Trigonometric Identities: How to Derive / Remember Them - Part 1 of 3.
Trigonometric Identities: How to Derive / Remember Them - Part 2 of 3.
Trigonometric Identities: How to Derive / Remember Them - Part 3 of 3.
Fundamental Trigonometric Identities
The reciprocal identities, quotient identities and the Pythagorean identities.
Deriving Trigonometric Identities from 3 Known Identities
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