# StudySquare

# Small angle approximations for SQA Higher Maths

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 360º, or 2π radians in a full turn.

The small-angle approximations are estimates of the basic trigonometric functions, valid when θ ≈ 0 and θ is in radians.

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

# 1

Given that θ is small and is measured in radians, use the small angle approximations to find the approximate value of (1 − cos4θ)/(2θsin3θ).

4/3

# 2

How many degrees are there in 2/3π radians?

120

# 3

Using the small-angle approximations, sinθ/cosθ × A = θ. What trigonometric function is A?

cosθ

# 4

Given that θ is small and is measured in radians, find (2θtanθ)/sin6θ.

θ/3

# 5

State the value of y.

180/π

End of page