Question

(1 point) Fit a trigonometric function of the form f(t) ,5), using least squares c1 sin(t) + c2 cos(t) to the data points (0, -1), (,7), (n, 5), co Co = C1 C2

Answer 1

Fita higovonehic Anctang the ferm fct): co+Cisint+cost to the data Painte Co,-1). C,)CT 5), (3 5using leagt sauee Sol: we want to fircl a +15nt+ast Such that fet) fco)-1,FC7, fCT) -5, )-S The candhas give the sytem gf lineen eauados Cot Sin Co)+ C2cos Co) -1 Cote,Sin CT)+C2 COSCT)- 5 Cot e Co+Ci C 2-5 co-Ci5 Let A: 1 aud 1-Io we com wide the sygtom 08 AcB. Since 7nefCA): - R2-R2-R,, RaR-R, R4R-R o-2 -1-I R4+R2 C -2 - oN T 0-0T 0-00 -o00 000

R3- /-2 F 11 RIRI-R3 O (t kerA)-fo? Z-B So the uniaue leay t-sauase Ne have 2:(ATA)AS Solo hon f A -1 o-1 o-1 find C C C R3-R3 /2 Ri-) RI/4 O 1/4 I 0-O 0-0 0 O - 0 0 -o 0 O 0 o o to odo - o 0 O

1 O 16 .Co=4 CI C2:-3 MOTONenthe tgononetie fnctor, fCt) + Sint- 3cat ANS Co = CIE -2- -3 t-3