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Stitz-Zeager_College_Algebra_e-book

# Hence cos arccos 3 cost 3 5 5 5 704 foundations

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Unformatted text preview: − β0 ) = cos(α0 ) cos(β0 ) + sin(α0 ) sin(β0 ). Since α and α0 , β and β0 and α − β and α0 − β0 are all coterminal pairs of angles, we have cos(α − β ) = cos(α) cos(β ) + sin(α) sin(β ). For the case where α0 ≤ β0 , we can apply the above argument to the angle β0 − α0 to obtain the identity cos(β0 − α0 ) = cos(β0 ) cos(α0 ) + sin(β0 ) sin(α0 ). Applying the Even Identity of cosine, we get cos(β0 − α0 ) = cos(−(α0 − β0 )) = cos(α0 − β0 ), and we get the identity in this case, too. To get the sum identity for cosine, we use the diﬀerence formula along with the Even/Odd Identities cos(α + β ) = cos(α − (−β )) = cos(α) cos(−β ) + sin(α) sin(−β ) = cos(α) cos(β ) − sin(α) sin(β ) We put these newfound identities to good use in the following example. Example 10.4.1. 1. Find the exact value of cos (15◦ ). 2. Verify the identity: cos π 2 − θ = sin(θ). Solution. 1. In order to use Theorem 10.13 to ﬁnd cos (15◦...
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