5.3 Sum and Difference Formulas sin(u+v)= sinu cosv + cosu sinv ...
5.3 Sum and Difference Formulas sin(u+v)= sinu cosv + cosu sinv ...
5.3 Sum and Difference Formulas sin(u+v)= sinu cosv + cosu sinv ...
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<strong>5.3</strong> <strong>Sum</strong> <strong>and</strong> <strong>Difference</strong> <strong>Formulas</strong><br />
<strong>sin</strong>(<strong>u+v</strong>)= <strong>sin</strong>u <strong>cosv</strong> + <strong>cosu</strong> <strong>sin</strong>v<br />
<strong>sin</strong>(u-v) = <strong>sin</strong>u <strong>cosv</strong> - <strong>cosu</strong> <strong>sin</strong>v<br />
cos(<strong>u+v</strong>)= <strong>cosu</strong> <strong>cosv</strong> - <strong>sin</strong>u <strong>sin</strong>v<br />
cos(u-v) = <strong>cosu</strong> <strong>cosv</strong> + <strong>sin</strong>u <strong>sin</strong>v<br />
tan(<strong>u+v</strong>) = tanu + tanv<br />
1 - tanu tanv<br />
tan(u-v) = tanu - tanv<br />
1 + tanu tanv<br />
February 26, 2013
February 26, 2013
Write the expression as the <strong>sin</strong>e, co<strong>sin</strong>e, or tangent of an<br />
angle.<br />
1. cos94 o cos18 o +<strong>sin</strong>94 o <strong>sin</strong>18 o<br />
2. tan 3x - tan 2y<br />
1 + tan 3x tan 2y<br />
February 26, 2013
Examples. Simplify.<br />
1. cos( - x )<br />
February 26, 2013
2. Confirm the cofunction identity.<br />
<strong>sin</strong> ( - x ) = cos x<br />
2<br />
February 26, 2013
3. Find the exact value of <strong>sin</strong> 15.<br />
February 26, 2013
4. Find the exact value of cos<br />
12<br />
February 26, 2013
5. Find the exact value of <strong>sin</strong> (u + v) given:<br />
<strong>sin</strong> u = 4 0 < u <<br />
5 2<br />
cos v = -12 < v <<br />
13 2<br />
February 26, 2013
Evaluate:<br />
cos (arctan 1 + arccos x)<br />
February 26, 2013
Prove the identity.<br />
cos (x+h) - cos x cos h - 1 <strong>sin</strong> h<br />
=<br />
cos x - <strong>sin</strong> x<br />
h h h<br />
February 26, 2013
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