Trigonometric Identities and Definitions

Reciprocal Identity for cosecant

• @@rac{1}{ an heta}@@

• @@rac{1}{ ext{cos} heta}@@

• @@rac{1}{ ext{sin} heta}@@

• @@rac{1}{ ext{sec} heta}@@

Evaluate the limit: @@\lim_{\theta \to -\frac{\pi}{2}} \frac{\cos^2 \theta}{1 - \sin \theta}@@

• 0

• 1

• -1

• undefined

Evaluate the limit: @@\lim_{\theta \to -\frac{\pi}{2}} \frac{\cos \theta}{\cot \theta}@@

• 0

• 1

• -1

• undefined

Quotient Identity for tangent

• @@ an heta = rac{ an heta}{1}@@

• @@ an heta = rac{ an^2 heta}{1}@@

• @@ an heta = rac{ an heta}{ an heta}@@

• @@ an heta = rac{ ext{sin} heta}{ ext{cos} heta}@@

Quotient Identity for cotangent

• @@rac{ ext{sin} heta}{ ext{cos} heta}@@

• @@rac{ ext{cos} heta}{ ext{sin} heta}@@

• @@rac{ ext{tan} heta}{ ext{sec} heta}@@

• @@rac{ ext{sec} heta}{ ext{tan} heta}@@

• 0

• 1

• -1

• undefined

Reciprocal Identity for sine

• @@rac{1}{ an heta}@@

• @@rac{1}{ ext{sec} heta}@@

• @@rac{1}{ ext{csc} heta}@@

• @@rac{1}{ ext{cot} heta}@@

Limit of @@3tan \theta cos \theta@@ as @@\theta approaches -\frac{3\pi}{2}@@

• -3

• 0

• 3

• -1

Pythagorean Identity involving sine and cosine

• @@rac{1}{2}@@

• @@ an^2 heta + 1 = rac{1}{ ext{cos}^2 heta}@@

• @@rac{ ext{sin}^2 heta}{ ext{cos}^2 heta} + 1 = ext{sec}^2 heta@@

• @@ ext{sin}^2 heta + ext{cos}^2 heta = 1@@

Definition of cotangent in terms of sine and cosine

• Cotangent is the ratio of sine to cosine.

• Cotangent is the product of sine and cosine.

• Cotangent is the ratio of cosine to sine.

• Cotangent is the difference between sine and cosine.