Inverse trigonometric functions

The diagram shows the graph of y = arctan x

The graph has horizontal asymptotes at y = –a and y = a

State the value of a

Circle your answer.

One of the diagrams below shows the graph of y = arccos x

Identify the graph of y = arccos x

Tick () one box.

The function f is defined by

The curve with equation y f (x) is shown below.

State the value of a

On the diagram above, sketch the curve with equation

and

sketch the line with equation

Explain why the solution to the equation

must also be a solution to the equation

Use the Newton-Raphson method with x₀ 0 to find an approximate solution, x₃, to the equation

Give your answer to four decimal places.

The graph of y arccos x is shown.

State the coordinates of the end point P.

Circle your answer.

equation

has exactly one solution for x 0

By considering a suitable change of sign, show that the solution to the equation lies between 0.4 and 0.6

Show that the equation can be rearranged to give

Use the iterative formula

with x 04, to find x, x and x, giving your answers to four decimal places. 1 2 3 4

On the graph below, draw a cobweb or staircase diagram to show how convergence takes place, indicating the positions of x, x and x.

f (x) arcsin x

State the maximum possible domain of f

Tick () one box.