Trigonometric Formulae & Identities (Edexcel IGCSE Further Pure Maths): Exam Questions

Figure 2 shows a right pyramid with a horizontal square base of side 8 cm. The vertical height of the pyramid is cm and cm.

The midpoint of OA is P and Q is the point on BC such that BQ : QC = 3 :1

Find, to 1 decimal place, the size of angle .

Show that

Hence express in the form where and are integers, giving the value of and the value of ,

In triangle , = cm, cm and cm

The area of triangle is cm²

Find, to 2 decimal places, the value of

Figure 5 shows a right triangular prism where is a rectangle.

cm

Using a formula from page 2 (opens in a new tab),

show that

Without using a calculator,

show that cm

Using formulae (opens in a new tab), show that

Using formulae from page 2 (opens in a new tab), show that

Show that

Hence, or otherwise, solve, giving exact values in terms of

for

Triangle is such that

Given that angle is obtuse,

find, in cm to one decimal place, the length of

Using a formula (opens in a new tab), show that

Hence, solve the equation

for

Using a formula given on page 2, solve, giving your solutions as exact values

for

Figure 2 shows triangle

where

Find the area of triangle

Using a formula (opens in a new tab), show that

Using the formulae (opens in a new tab) , show that

(i)

(ii)

Show that

Solve, for the equation,

Give your answers to the nearest whole number.

Figure 3 shows a right triangular prism . A cross section of the prism is a triangle in which and radians.

In the prism

and radians.

Show that the volume of the prism is

Using formulae (opens in a new tab) , show that

(i)

(ii)

Show that

Solve, in radians to 3 significant figures, for , the equation

In triangle , , and

Find, in degrees to one decimal place, the size of

In triangle , , and

The area of triangle is 24 cm²

Find, to 3 significant figures, the value of

Figure 1 shows triangle in which

Find the value of

Give your answer in the form where and are integers to be found.

Using the formulae (opens in a new tab), show that

(i)

[2]

(ii)

[3]

Given that where

use the results from part (a) to show that can be written as

Solve for