Principled Maths

Y2 Pure, Chapter 6:

Trigonometric functions

Y2 Pure Chp6 KO.pdf

Knowledge organiser

Y2 Pure - Chp6 Trigonometric Functions.pdf

Textbook chapter

Y2 Pure Chp6 Solutions.pdf

PMT solutions

Y2 Pure 6.1

Secant, cosecant and cotangent

Intro: cosec(x), sec(x) & cot(x)

Given sin(x) = 3/7, exact values of cosec(x), sec(x) & cot(x)

Y2 Pure 6.2

Graphs of sec(x), cosec(x) and cot(x)

Sketching y = cosec(x)

Sketching y = sec(x)

Sketching y = cot(x)

+E4-06 (transformations)

Y2 Pure 6.3

Using sec(x), cosec(x) and cot(x)

Solve cosec(x) = 5

between 0 and 2π radians

Solve sec(x) = 7

between 0 and 2π radians

Solve cot(x) = 1/6

between 0 and 2π radians

Solve sec(x) = tan(x)

between 0 and 2π radians

Solve sin(x) = cot(x)

between 0 and 2π radians

Y2 Pure 6.4

Trig identities

Proving 1 + cot^2 θ = cosec^2 θ

Proving tan^2 θ + 1 = sec^2 θ

Simplifying further expressions

Solve sec^2(x) = 4 + 2tan(x) between 0 and 2π radians

Solve cosec^2(x) = 3cot(x) + 5 between 0 and 2π radians

Proving trigonometric identities: example 3

Proving trigonometric identities: example 4

+E8-06 (examples 5)

Y2 Pure 6.5

Inverse trig functions

Examples of two transformations of y = arccos(x)

Why we restrict the domain to find an inverse function

Intro: arcsin(x)

Intro: arccos(x)

+E5-04

Intro: arctan(x)

Transformations of arcsin(x), arccos(x) & arctan(x)

cos(arcsin(x)), tan(arccos(x)), cos(arctan(x))

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