PRECALC ALG & TRIG
PRECALC ALG & TRIG MAC 1147
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This 9 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1147 at University of Florida taught by Larissa Williamson in Fall. Since its upload, it has received 9 views. For similar materials see /class/207048/mac-1147-university-of-florida in Calculus and Pre Calculus at University of Florida.
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Date Created: 09/19/15
L21 Sum and Difference Formulas Doubleangle and Halfangle Formulas Solving Right Triangles Sum and Difference Identities Caution cos02 c0502 cos for arbitrary angles 02 and 37239 7239 Example cos 7 7239 cos cos 7239 Sum and Difference Formulas for Cosines cos02 cosacos sinasin cos02 cosacos sin02sin Example Find the exact value of cosi g Sum and Difference Formulas for Sines sin02 sinacos cosasin sin02 sinacos cosasin Example Simplify 7239 sm 6 2 Example Find the exact value of 27239 7239 27239 7239 cos cos s1n s1n 5 10 5 10 Example Given that coss sis in quadrant HI and MIDI e Evaluate 3 cos sin 1 E cos 1 sint 2 t is in quadrant IV Find 13 17 sinst Sum and Difference Formulas for TangentS39 Doubleangle and Halfangle Formulas t t tana ana an l tanatan tana tana tan ltanatan sin26 Example Find the exact values of 00526 tan105 tan80 tan 55 ltan80 tan 55 tan26 Example Verify the identity Doubleangle Formulas 2 sec2 6 sin26 25in6cos6 COSZ secz 00526 cos2 6 sin2 6 00526 Zoos2 6 1 00526 1 25in2 6 tan 26 Ztan g Example Find the exact value of l tan2 6 1 4 cos 2tan g Example Find the exact value of ZSlHZCOSZ 6 6 2005215 l Halfangles Formulas Solving cos 26 l 2sin2 6 for sin2 6 we have Sin2621 00526 2 then sin6 iJ Let 6 then 26 0 and SingziJl cosa 2 2 Solving cos 26 20052 6 l for cos2 6 we have COS2 6 lcos26 2 then 0056 iJ Let 6 2 then 26 0 and 2 cosgziJlcosa 2 2 sin2 6 a Since tan2 6 2 nd cos 6 sin26z 0526MWe have tan2621 00526 lcos26 then tan 6 i M l cos 26 Let 6 then 26 0 and 0 l cosa tan i 2 lCOSOl Also a a a a a 8111 20057 251nicosi Sina cosi 20057 200527 0050 2 2 2 a a a 8111 251n7 251n27 1 tan 2 22 22 a a a a 39 cosi 251n7 251nicosi gm 2 2 2 2 0 sinot 0 l cosa tan 2 or tan 2 lCOSOl 2 1110 Example Use the Halfangle Formula to nd cosg SOlvmg nght Trlangles I 6 Example If tan z 7 Elt lt 7239 nd cotE a2 b2 02 a 290 Example If a 3 and b 5 nd 0 a and Round your answers to one decimal place Example If a 2 and 20 nd b c and a Round your answers to one decimal place The acute angle measured from horizontal to lineof sight observation ofthe object is called the angle ofelevation or angle ofdepression LL Example Find the height of the mountain ifthe angle of elevation to the top is 43 and then changes to 32 when the surveyor moves 750 ft father away summit Example A helicopter hovers 800 ft above a small island offthe Florida coast The pilot takes a sighting to a pointP on the edge ofthe mainland If the angle of depression is 35 how far offthe coast is the island Island P Example What is the angle of elevation of the sun when a 35 ft mast casts a 20 ft shadow Example An aerial photographer who photographs farm properties for a real estate company has determined that the best photo is taken at a height of 475 feet and at a distance from the airplane to the house of 850 feet What is the angle of depression from the plane to the house Example A new tee shirt design is to have a regular pentagon inscribed in a circle Each side of the pentagon is to be 35 in long Find the radius of circumscribed circle