Question

Find an equation for the line tangent to the curve at the point defined by the given value oft. Also, find the value of dy at this point x=++ cost, y = 1 + 2 sin tt-7 Write the equation of the tangent line. y=-x+ (Type exact ahswers, using as needed)

Answer 1

Solution, N=++ cost Y = B densint, It 2 Sint t=16 da d (t + cost) dt dt - I-Sint dy dt =후 1+25int) dt 2 cost dy da = 1 dyldt daldt 2 cost Sint

Compute the first derivative and use these to Compute dylda (k) - ㅠ 6 + Cos( le) ㅠ t J3 2 T十33 G =1425in(E ST) - 1+2() C2 dy = 머 2 (5) 1-sin( 1. 2 13 - 23

9-2= 253 (x- (T + 35 9-22 1522 - bus +" 9-2= 2530-/2153 + 18 + 2 ya 12131 - 2153-18 6 y= 12532-21553 -18712 6 2 y = 12530 12531 -10.8-6 6 Ang? y= 3,462-16,8 y = 3.467 - 16.8