Question

y=sin x
Sketch. Find tangent and normal at:
a) x=2pi/3
b) x=pi/2
c) x=pi/6

I'm not sure how to scale the graph. I have put the x values into sin x and have points. Not sure about this tangent and normal.

Please help!

Answer 1

y = sin x
dy/dx = slope of tangent = cos x

at x = 2 pi/3
y = sin 2 pi/3 = .5 sqrt 3

slope = cos 2 pi/3 = .5
so equation of tangent
y = .5 x + b
.5 sqrt 3 = pi/3 + b
b = .5 sqrt 3 - pi/3
= -.181 approximately
so for the tangent line
y = .5 x - .181

for normal m' = -1/m = -2
y = -2 x + b
put the point in again
.5 sqrt 3 = -2 (2 pi/3) + b
.5 sqrt 3 = -4 pi/3 + b
b = .5 sqrt 3 + 4 pi/3
= 5.05
y = - 2 x + 5.05

Do the others the same way