Trigonometric Graphs & Equations (AQA GCSE Further Maths)

Here is a sketch of       for  

You are given that

Work out the two values offor  for which 

[2]

Work out the value of where  for which 

[2]

Show that can be written in the form   

where andare integers.

[4]

Here is a sketch graph of  for  

You are given that    cos 36° = 0.8090

Solve cos = −0.8090    for   0° ⩽ ⩽ 360°

[2]

Show that  is equivalent to tan

[3]

Hence solve   for  

[2]

Here is a sketch of 

How many solutions of tan  where  are between 90° and 360° ?

[1]

How many solutions of  are between 0° and 180° ?

You may use a sketch graph to help you.

[1]

State the coordinates of each point where the graph

meets or intersects an axis.

[2]

Work out the size of angle .

 ........................ degrees[3]

        where A and B are integers.

Work out the values of A and B.
You must show your working.

A = ........................... B = ...........................[2]

Angle θ is obtuse and
Work out the value of cos .

[4]

Angle is acute.

where is a constant greater than 1

Which of the statements below is correct?

Circle your answer.

[1]

                     could be any acute angle

Prove that  

[2]

Hence, or otherwise, work out the values of between and  for which

[4]