Secant, cosecant and cotangent

One of the diagrams below shows the graph of y = cosec x° for 0 ≤ x ≤ 360

Identify the correct graph.

Tick () one box.

Given that cos 1, prove the identity

Hence, find the set of values of A for which the equation

has real solutions.

Fully justify your answer.

Given that is obtuse and

find the exact value of cot

Sketch the graph of

Given that

show that

Hence, solve

in the interval 0 2

Give your answers to two decimal places.

Solve

Give your answers to one decimal place.

Which one of the following equations has no real solutions?

Tick () one box.

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.

Show that the equation

can be written in the form

Hence, given x is obtuse and

find the exact value of tan x

Fully justify your answer.

p(x) 30x³ 7x² 7x 2

Prove that (2x 1) is a factor of p(x)

Factorise p (x) completely.

Prove that there are no real solutions to the equation