Question

Let f(x)= √1-sinx)

(a.) What is the domain of x?
(b.) Write an equation for the tangent line to the graph of f at x=0.

I mostly just need help with letter B. I think I can get letter a.

Answer 1

f(x)=sqrt(1-sin(x))
Find derivative with respect to x (need to use chain rule):
f'(x) = -(1/2)cos(x)/sqrt(1-sin(x))
At x=0,
f(0)=1
f'(0)=-1/2 (=slope)
Therefore the line of the tangent has a slope of m=-1/2 and passes through (0,1)=(x0,y0).
The standard formula for a line with slope m passing through (x0,y0) is:
y=m(x-x0)+y0

Hope you can take it from here.