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linear approxi chen versus differenhel approximahen Approximate. sin 29° = sin(? 5p). 297 15 close to 30°= oF g where we know the sine and curine exachy , so eithec #0 appreximahon should use 30° as the reference port linear a pproximathon at x= T/C: differenhal approx maton y= F&)= sink | y= f(¥)e nas Step 4 ys F(X) = sinx { = ' =o; t- B di _ F(x = C05 x 3 Q)sesF= SB Ba Sy = (OSX et. (84) sbpe G dy= F'Oddx = esxdx rite eq. of ban line. ah x=: ud 2 Bly ie = GOe%) dy = csEdx= 12 dx = By-t ne 3 2* B(x ) dy = 29°- 30° = -\°s-L . ew al. Tai Lx) = 3 + & (x-B) linear apprximation " ceferce \go now at X= 29° Wir Slo) LOID= £4 BE AE a CA ho 0.50000 — 6,015 0,4 8489 compare wrth 5 £(29°) = sin 29° = 0A 8464 it ys le) 4 y=sinx x c cleacly linear approximation ts fro high | romenter, derivahve formulas | for trig Functions assume | angles Ore given in radians. calculahon mustbe done tn radians. then dy = g CS) == 0.0151 step 2: at xeWet minus ys f(%)= sn = 4 + degree = 0.50060 new valve of y = did valve plus change: Ut dy = O50000— 6.01511 0.48489 [dane] i K compare with: ay = sin 29° ~ on 30° change MO = 0.015194 Y= -0-0151 the differeninal apprexiinatien is toohigh (less negahve Bx dx < 0 ys Lo) ay \° f Y= Fe) 29° 30° 
