Β 
VIEW IN FULL SCREEN

AQA A-level Maths Small angle approximations

Small angle approximations

This page covers the following topics:

1. Radians
2. Introduction to small angle approximations
3. Small angle approximations

Like degrees, radians are an alternative unit for measuring angle. There are 360ΒΊ, or 2Ο€ radians in a full turn.

Radians

The small-angle approximations are estimates of the basic trigonometric functions, valid when ΞΈ β‰ˆ 0 and ΞΈ is in radians.

Introduction to small angle approximations

We can use the small-angle approximations to solve more complicated algebraic expressions.

Small angle approximations

1

Given that ΞΈ is small and is measured in radians, use the small angle approximations to find the approximate value of (1 βˆ’ cos4ΞΈ)/(2ΞΈsin3ΞΈ).

Given that ΞΈ is small and is measured in radians, use the small angle approximations to find the approximate value of (1 βˆ’ cos4ΞΈ)/(2ΞΈsin3ΞΈ).

2

How many degrees are there in 2/3Ο€ radians?

How many degrees are there in 2/3Ο€ radians?

3

Using the small-angle approximations, sinΞΈ/cosΞΈ Γ— A = ΞΈ. What trigonometric function is A?

Using the small-angle approximations, sinΞΈ/cosΞΈ Γ— A = ΞΈ. What trigonometric function is A?

4

Given that ΞΈ is small and is measured in radians, find (2ΞΈtanΞΈ)/sin6ΞΈ.

Given that ΞΈ is small and is measured in radians, find (2ΞΈtanΞΈ)/sin6ΞΈ.

5

State the value of y.

State the value of y.

End of page

Β