Today in class, we talked about An identity is an equation that is satisfied by every number for which both sides are defined. Identities can help combine terms when dividing and multiplying. There are infinitely trigonometric identities, but only the most common identities should be memorized.
Reciprocal Identities
sin(x)=1csc(x) cos(x)=1sec(x) tan(x)=1cot(x)
csc(x)=1sin(x) sec(x)=1cos(x) cot(x)=1tan(x)
Tangent and Cotangent in Terms of Sin and Cosine
tan(x)=sin(x)cos(x)
cot(x)=cos(x)sin(x)
Pythagorean Identities
sin2(x)+cos2(z)=1
1+cot2(x)=csc2(x)
tan2(x)+1=sec2(x)
Odd/Even Identities
An odd function is one for which f(-x)=-f(x) and an even function is one for which f(-x)=f(x)
Odd Identities:
sin(-x)=-sin(x)
csc(-x)=-csc(x)
tan(-x)=-tan(x)
cot(-x)=-cot(x)
Even Identities:
cos(-x)=cos(x)
sec(-x)=sec(x)
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