# Thread: find a and b

1. ## find a and b

Let f(x) = A sin ((2pi/B)*X)
.The graph of this function has a tangent line with a slope of 4
at the point (B/8 , 1)
find the exact values of a and b

so for a i put in B/8 for x and 1 for y and cancled out the b's and got
a= 1/sin(pi/4)

then for b do i find the derivative and make that = 4?
or is b infinate?

2. Originally Posted by valvan
Let f(x) = A sin ((2pi/B)*X)
.The graph of this function has a tangent line with a slope of 4
at the point (B/8 , 1)
find the exact values of a and b

so for a i put in B/8 for x and 1 for y and cancled out the b's and got
a= 1/sin(pi/4)

then for b do i find the derivative and make that = 4?
or is b infinate?
That's a good start and looks ok. Remember that $\displaystyle \sin \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt2}$ and hence $\displaystyle \csc \left(\frac{\pi}{4}\right) = \sqrt{2}$

$\displaystyle f'(x) = 4$

$\displaystyle \frac{d}{dx} \left[ \sqrt2 \sin \left(\frac{2\pi x}{B}\right) \right]$

$\displaystyle = \frac{2 \pi \sqrt{2} }{B} \cos \left(\frac{2\pi x}{B}\right) = 4$

It appears you'll need to use an iterative method