Questions from General Calculus

Q: Find the exact value of each expression. a. arcsin

Find the exact value of each expression. a. arcsin(sin(5π/4)) b. cos(2 sin-1 (5/13))

Q: Prove that cos(sin-1 x) = 1

Prove that cos(sin-1 x) = 1 − x2 .

Q: Simplify the expression. tan(sin-1x)

Simplify the expression. tan(sin-1x)

Q: Simplify the expression. sin(tan-1x)

Simplify the expression. sin(tan-1x)

Q: Simplify the expression. sin(2arccosx)

Simplify the expression. sin(2arccosx)

Q: Graph the given functions on the same screen. How are these

Graph the given functions on the same screen. How are these graphs related? y = sin x, -π/2 ≤ x ≤ π/2; y = sin-1x; y = x

Q: Graph the given functions on the same screen. How are these

Graph the given functions on the same screen. How are these graphs related? y = tan x, -π/2 < x < π/2; y = tan-1x; y = x

Q: Find the domain and range of the function g(x

Find the domain and range of the function g(x) = sin-1(3x + 1)

Q: a. Graph the function f(x) = sin(

a. Graph the function f(x) = sin(sin-1x) and explain the appearance of the graph. b. Graph the function g(x) = sin-1(sin x). How do you explain the appearance of this graph?

Q: a. If we shift a curve to the left, what

a. If we shift a curve to the left, what happens to its reflection about the line y = x? In view of this geometric principle, find an expression for the inverse of g(x) = f(x + c), where f is a one-to...