Trigonometric Equations (Edexcel International AS Maths: Pure 2): Exam Questions

Find all solutions to the equation in the interval , giving your answers in radians as multiples of

Find all solutions to the equation in the interval , giving your answer in radians to three significant figures.

Show that the equation can be written in the form , where and are integers to be found.

Hence, or otherwise, solve the equation for

Given that , find the possible values of and

Solve the equation for

Solve the equation for

A right-angled triangle has hypotenuse 8 cm. One of its other sides is 5 cm.

Find exact values for and , where is the smallest angle in the triangle.

Solve the equation for

Show that

Hence, or otherwise, solve the equation for , giving your answers to 1 decimal place where appropriate.

A seagull sits on the surface of the sea and moves up and down as waves pass.

Its height, metres, above its position in calm water is modelled by the function where is the time in seconds after timing commences.

Sketch a graph of against for showing the coordinates of the points of intersection with the - axis

How many times in the first minute after timing commences is the seagull 0.25 metres above its calm water position?

Find the time at which the seagull is first 0.25 m above its calm water position and moving downwards. Give your answer to 3 significant figures.

Solve the equation for

Solve the equation in the interval , giving your answers to 3 significant figures.

Solve the equation for , giving your answers to 1 decimal place where appropriate.

Given that the angle is reflex and that ​, find the exact value of .

Solve the equation for ​.

Solve the equation for , giving your answers to 1 decimal place where appropriate.

For the triangle in the diagram, find exact values for , and .

Find all the values of in the range which satisfy the equation

, giving your answers to 1 decimal place.

Find all the solutions to the equation

in the interval , giving your answers in radians as multiples of .

Find all the solutions to the equation in the interval , giving your answers in radians to three significant figures.

A seagull sits on the surface of the sea and moves up and down as waves pass.

Its height, metres, above its position in calm water is modelled by the function where is the time in seconds after timing commences.

Find the amount of time the seagull is more than 0.5 metres above its calm water position in the first 20 seconds after timing commences.

Give your answer correct to 3 significant figures.