Reciprocal & Inverse Trigonometric Functions (A Level only) (OCR A Level Maths: Pure)

Use the definitions of the secant, cosecant and cotangent functions to show that

sec  cot cosec .  

Hence solve, in the range , the equation

sec  cot 

Show that the equation

sec 

can be rewritten in the form

Hence solve, in the range , the equation

sec 

Using the double angle formula sin sin cos , show that the equation

sec  cosec cosec 

can be rewritten in the form

coesec .

Hence solve, in the range , the equation

sec  cosec cosec 

giving your answers correct to 3 significant figures.

Show that the equation

tan²  sec 

can be rewritten in the form

Hence solve, in the range , the equation

tan²  sec 

giving your answers correct to 3 significant figures.

Given that  satisfies the equation  , where   

state the range of possible values of ,

express both sin and tan  in terms of .

 ,

Prove that for ,  .

Explain why this is not true for .

The function   is defined as   , , and the function    is such that  .

Sketch the graph of   and state the range of  .

Sketch the graph of    and state the domain of  .

Find the inverse function and state its domain.

Rewrite tan cosec as a single trigonometric function.

Hence solve, in the range , the equation

tan  cosec 

Solve, in the range , the equation

Using the double angle formula sin sin  cos ,  find the solutions to the equation

sec  cosec  cosec 

in the range .   Give your answers correct to 3 significant figures.

Show that the equation

cot² cosec

can be rewritten in the form

Hence solve, in the range , the equation

cot² cosec

giving your answers correct to 3 significant figures.

Given that  satisfies the equation   , where    ,

state the range of possible values of ,

express both cos and tan  in terms of .

Prove that for ,  .

Sketch, in the interval , the graph of  sec   , include asymptotes and label the coordinates of all maximum and minimum points.

Hence deduce the range of values for  for which the equation   sec    has no solutions.

The function    is defined as   ,    , and the function    is such that    .

Sketch the graph of and state the range of  .

Sketch the graph of and state the range of  .

Find the inverse function and state its domain.

Solve, in the range , the equation

Solve, in the range , the equation

sec

Leaving your answers as exact values.

Using the double angle formulae  and ,  find the solutions to the equation

in the range .   Give your answers correct to 3 significant figures.

Solve, in the range , the equation

Leaving your answers as exact values.

Given that  satisfies the equation  , where    

state the range of possible values of ,

express both sin and cos in terms of .

Prove that for ,

Sketch, in the interval , the graph of   , include asymptotes and label the coordinates of all maximum and minimum points.

Deduce the maximum and minimum values of  .

The function    is defined as  ,   , and the function    is such that 

Sketch the graph of and state the domain and range of  .

Define the inverse function in the form  … 

Over the same domain as  , the function  is defined as  .

Given that  for all  in the two functions’ common domain, determine the values of  and .