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Small angle approximations for SQA Higher Maths

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 360ยบ, or 2ฯ€ radians in a full turn.

Radians

The small-angle approximations are estimates of the basic trigonometric functions, valid when ฮธ โ‰ˆ 0 and ฮธ 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 ฮธ is small and is measured in radians, use the small angle approximations to find the approximate value of (1 โˆ’ cos4ฮธ)/(2ฮธsin3ฮธ).

4/3

Given that ฮธ is small and is measured in radians, use the small angle approximations to find the approximate value of (1 โˆ’ cos4ฮธ)/(2ฮธsin3ฮธ).

2

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

120

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

3

Using the small-angle approximations, sinฮธ/cosฮธ ร— A = ฮธ. What trigonometric function is A?

cosฮธ

Using the small-angle approximations, sinฮธ/cosฮธ ร— A = ฮธ. What trigonometric function is A?

4

Given that ฮธ is small and is measured in radians, find (2ฮธtanฮธ)/sin6ฮธ.

ฮธ/3

Given that ฮธ is small and is measured in radians, find (2ฮธtanฮธ)/sin6ฮธ.

5

State the value of y.

180/ฯ€

State the value of y.

End of page

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