My Math Forum calculating direction of tangent

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 March 11th, 2014, 01:06 PM #1 Member   Joined: Jan 2014 Posts: 40 Thanks: 0 calculating direction of tangent a) Given the function g(x) = sin^2(x), what is the direction of its tangent at some x =xo? I seem to be running into trouble with this one. I have used a value of 5 for x. using this formula y-f(xo)= f'(xo)(x-xo) f'=2(sinx)(cosx) sub for 5 and get -0.544 f(x) at 5 = 0.9195 Thus far I have y-0.9195 = -.544(x-5) y-0.9195= -0.544x + 2.72 y= -0.544x+3.64 When I plot this function I have a slope the looks around -.5 but why am I getting +3.64?
 March 11th, 2014, 06:41 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,659 Thanks: 2635 Math Focus: Mainly analysis and algebra Re: calculating direction of tangent That is where the tangent to $\sin^2{x}$ at x = 5 intercepts the y-axis. http://fooplot.com/plot/ooyzvg8bmj
 March 11th, 2014, 10:21 PM #3 Member   Joined: Jan 2014 Posts: 40 Thanks: 0 Re: calculating direction of tangent Thank you very much, makes perfect sense!

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