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In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles .
In this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions.
All the trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side.
The following is a list of useful Trigonometric identities: Quotient Identities, Reciprocal Identities, Pythagorean Identities, Co-function Identities, Addition Formulas, Subtraction Formulas, Double Angle Formulas, Even Odd Identities, Sum-to-product formulas, Product-to-sum formulas.
Opposite. Sine, Cosine and Tangent. The three main functions in trigonometry are Sine, Cosine and Tangent. They are just the length of one side divided by another. For a right triangle with an angle θ : Sine Function: sin (θ) = Opposite / Hypotenuse. Cosine Function: cos (θ) = Adjacent / Hypotenuse. Tangent Function: tan (θ) = Opposite / Adjacent.
Trigonometric identities include reciprocal, Pythagorean, complementary and supplementary, double angle, half-angle, triple angle, sum and difference, sum and product, sine rule, cosine rule, and a lot more. Learn all trig identities with proofs.
16 wrz 2022 · For example, one of the most useful trigonometric identities is the following: \[ \tan\;\theta ~=~ \frac{\sin\;\theta}{\cos\;\theta} \qquad \text{when } \cos\;\theta \ne 0 \label{3.1} \] To prove this identity, pick a point \((x,y) \) on the terminal side of \(\theta \) a distance \(r >0 \) from the origin, and suppose that \(\cos\;\theta \ne 0 \).
