Find the equation of the tangent line to the graph at t = pi/2
y=_____x + _______
Please explain b/c i thought the derivative would be
cos(12*pi/2) * 12 + 5 - sin(pi/2) = 16 but the 16 isnt the answer!
2007-09-09 14:41:07 · 5 answers · asked by zahras01 1 in Science & Mathematics ➔ Mathematics
the derivative evaluated at pi/2 is suppose to be cos(12*pi/2)*12 + 5*(-sin(pi/2)) = 12+5(-1)=7... so use this to finish the problem
2007-09-09 14:49:23 · answer #1 · answered by brianhawking25 1 · 0⤊ 0⤋
f'(x) = 12· cos(12t) - 5·sin(t)
m=f'(pi/2) = 12·cos(6·pi) - 5·sin(pi/2) = 12· cos(0) - 5·sin(pi/2)
m=12·1-5·1 = 7
--> y=7x - 7·pi/2
saludos.
2007-09-09 21:58:09 · answer #2 · answered by lou h 7 · 0⤊ 0⤋
You almost got it.
The derivative is cos(12*pi/2) * 12 + 5*(- sin(pi/2)] = 12+5*(-1)=7.
2007-09-09 21:51:55 · answer #3 · answered by np_rt 4 · 0⤊ 0⤋
Your math is incorrect. The derivitive looks OK, but 12-5=7. With this slope and the point pi/2,0 you can figure out the line.
2007-09-09 22:16:15 · answer #4 · answered by cattbarf 7 · 0⤊ 0⤋
y = f(t) = sin (12t) + 5 cos(t)
y' = 12cos(12t) - 5 sin(t)
When t = pi/2, y' = 12sin (6pi) +5cos (pi/2) = 5
So y = 5x +b
when t = 0, f(t) = 5, so b=5
The equation is y = 5x+5
2007-09-09 22:07:30 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋