Express Sine in Terms of Cosine
Basic Pythagorean Identities for Trigonometry Functions
Using the Angle-Sum Identity

Cotangent and Cosecant Identities on a Unit Circle

Starting with the Pythagorean identity, sin2θ + cos2θ = 1, you can derive cotangent and cosecant Pythagorean identities. All you do is throw in a little algebra and apply the reciprocal and ratio identities and — poof! — two new identities.

  1. Starting with the first Pythagorean identity, sin2θ + cos2θ = 1, divide each term by sin2θ.

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  2. Rewrite each term.

    image1.png
  3. Replace each of the terms with an equivalent expression.

    image2.png

    Substituting these expressions into the equation and simplifying, you find that the result is

    image3.png
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Sum-to-Product Identities
Break Up or Combine Fractions to Solve a Trigonometry Identity
Tangent and Secant Identities on a Unit Circle
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Rearrange the Pythagorean Identities
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