· Identities: an equation that is always true.
o Reciprocal Identity:
§ Ex)\[sin\theta =1/csc\theta \]
· (applies to all six)
o Quotient Identity:
§ Ex)\[tan\theta =sin\theta /cos\theta \]
· (applies to all six)
o Even Odd Identities
§ Ex)\[sin(-\theta )=-sin\theta \]
· (applies to all six)
o Pythagorean Identities
§ Three different identities
· 1) \[sin^2\theta +cos^2\theta =1\]
· 2) \[tan^2\theta +1=sec^2\theta \]
· 3) \[cot^2\theta +1=csc^2\theta \]
· Solving Identities:
o Ex) \[(cot\theta +csc\theta)(tan\theta -sin\theta)=sec\theta -cos\theta \rightarrow (1-cot\theta)(sin\theta)+(csc\theta)(tan\theta-1)\rightarrow -(cos\theta /sin\theta )(sin\theta )+(1/sin\theta)(sin\theta /cos\theta )\rightarrow -cos\theta +1/cos\theta \rightarrow sec\theta =cos\theta =sec\theta -cos\theta \]