# Rate of change using trig functions.

• Mar 14th 2010, 08:03 PM
youmuggles
Rate of change using trig functions.
An equation of the tangent line to the curve https://nernst.chem.sfu.ca/cgi-bin/m...0%5Csin%20x%29

at the point https://nernst.chem.sfu.ca/cgi-bin/m...283%20%5Cpi%29 is y =
(point intercept form: y = mx+b)

I know it's easier to fine f(3π) ans f'(3π) and then simplifty the exact value of sin(3π) and cos(3π)...

So I got

f(3π) = 3π((5cos(3π)-9sin(3π))) = -15π
f'(3π) = 3π(-5sin(3π)-9cos(3π))+5cos(3π)-9sin(3π) = -26.99

but I dont know what to do with these values and or if i've gone to correct way of solving this. any help would be wonderful!
• Mar 14th 2010, 08:25 PM
pickslides
Quote:

Originally Posted by youmuggles
An equation of the tangent line to the curve https://nernst.chem.sfu.ca/cgi-bin/m...0%5Csin%20x%29

at the point https://nernst.chem.sfu.ca/cgi-bin/m...283%20%5Cpi%29 is y =
(point intercept form: y = mx+b)

I know it's easier to fine f(3π) ans f'(3π) and then simplifty the exact value of sin(3π) and cos(3π)...

So I got

f(3π) = 3π((5cos(3π)-9sin(3π))) = -15π
f'(3π) = 3π(-5sin(3π)-9cos(3π))+5cos(3π)-9sin(3π) = -26.99

but I dont know what to do with these values and or if i've gone to correct way of solving this. any help would be wonderful!

Your line will be

$y- f\left(\frac{\pi}{3}\right) = f'\left(\frac{\pi}{3}\right)\left(x-\frac{\pi}{3}\right)$
• Mar 14th 2010, 08:38 PM
sa-ri-ga-ma
Quote:

Originally Posted by youmuggles
An equation of the tangent line to the curve https://nernst.chem.sfu.ca/cgi-bin/m...0%5Csin%20x%29

at the point https://nernst.chem.sfu.ca/cgi-bin/m...283%20%5Cpi%29 is y =
(point intercept form: y = mx+b)

I know it's easier to fine f(3π) ans f'(3π) and then simplifty the exact value of sin(3π) and cos(3π)...

So I got

f(3π) = 3π((5cos(3π)-9sin(3π))) = -15π
f'(3π) = 3π(-5sin(3π)-9cos(3π))+5cos(3π)-9sin(3π) = -26.99

but I dont know what to do with these values and or if i've gone to correct way of solving this. any help would be wonderful!

The point on the curve, where the tangent is drawn, is (3π, -15π)
The slope of the tangent is (27π - 5 )
Now the equation of the tangent is
(y-y1) = m(x-x1)
Substitute the values to get the answer.