S56 (5.3) Addition Formulae.notebookmissdeely.weebly.com/.../higher_addition_formulae.pdf · S56 (5.3) Addition Formulae.notebook February 09, 2016 1. Daily Practice 4.2.16 Today

S56 (5.3) Addition Formulae.notebook February 09, 2016

Daily Practice 28.1.2016

Q1. Given f(x) = 3x + 2 and g(x) = 2x2 . Find expressions for f(g(x))

and g(f(x))

Q2. State the equation of the line that makes an angle of 450 with the positive direction of the x - axis and passes through (-1, 0)

Today we will be learning about Addition Formulae.

Homework Due Tuesday

Addition Formulae

Addition formulae is all about expanding trig. functions that contain compound angles. Eg. Sin (α + β)

We expand these because then we can evaluate them using our knowlege of right-angled trig.

Sin(A + B) = SinACosB + CosASinB (Proof not necessary)

Examples

1) Simplify sin45˚cos15˚ + cos45˚sin15˚

Sin(A + B)

Sin(A + B) = SinACosB + CosASinB

Examples

2) Find the exact value of Sin750

Sin(A + B)

Sin(A + B) = SinACosB + CosASinB

3) Given that C and D are acute angles where Sin C = and

Sin D =

Show that Sin (C + D) =

Sin(A + B)Sin(A + B) = SinACosB + CosASinB



Q1. State the equation of the perpendicular bisector of (-1, 2)

and (3, -6)

Q2. Vectors u and v are defined u = 3i + 2j and v = 2i - 3j + 4k

Determine whether or not u and v are perpendicular

Today we will be continuing to learn about addition formulae.

Homework Online due 2.2.2016

Addition Formulae: Sin(A - B)

Sin(A - B) = SinACosB - CosASinB (Formula in exam)

This expansion is true because sin(-x) = -sinx and cos(-x) = cosx

Examples:

1. Find the exact value of Sin 1350

Sin(A - B)

2. Show that Sin(x - ) = -cosx

Addition Formulae: Cos(A ± B)

Cos(A + B) = CosACosB - SinASinB Cos(A - B) = CosACosB + SinASinB

Examples:

1. Expand Cos(3A + 2B)


Addition Formulae: Cos(A ± B)

2. Simplify cos 250˚cos 40˚ + sin 250˚sin 40˚

3. Given that E and F are acute angles with sin E = and

tan F = , show that cos (E + F) =


Q1.

Today we will be continuing to practise using addtion formulae. Homework due tomorrow.


1.

2. A function is defined by . Calculate the rate of change of

f(x) when x = ‐3

Today we will be learning about Trigonometric Identities.

Homework due today


Trigonometric Identities

Trig. Identities are proofs in which you must show that the left-hand side of an equation equals the right-hand side.

Start with the LHS and expand it until it is the same as the right-hand side.

cosA= tanA and cos2x + sin2x= 1Remember: sinA

Trigonometric Identities

Examples:

1.

2. Prove that sin(x + 300) - sin(x - 300) = cosx

Prove that = tan A + tan Bcos A cos Bsin (A + B)


Q1. State the equation of the line that passes through (‐1, 3) and is

perpendicular to ‐x + 2y = 3

Q2. State the limit to the recurrence relation Un+1 = 0.25Un + 4

Q3. Given Show that a and b are perpendicular

Today we will be learning about double angle formulae.

Homework Online due 9.2.16


1.


Today we will be learning about double angle formulae.

Homework due Tuesday.

Double Angle FormulaeThis formula is created when the angles are equal.

Sin(A + A)

Cos(A + A)

sin2A = 2sinAcosA

cos2A = cos2A - sin2A = 2cos2A - 1 = 1 - 2sin2A

Double Angle Formulae


• when you expand the angle is halved

• when you simplify the angle is doubled

• cos2 A means (cos A)2

• the formulas use sin A & cos A so expect to use SOHCAHTOA & right-angled triangles.

Double Angle Formulae Double Angle Formulae

Sin2A = 2SinACosA

Cos2A = cos2A - sin2A = 2cos2A - 1 = 1 - 2sin2A

Examples:

1. Expand sin6α

Double Angle FormulaeExamples:

2. Given that tanA = , Find the values of cos2A and sin2A

3. Find the exact value of 2cos222.50 - 1

Sin2A = 2SinACosA

Cos2A = cos2A - sin2A = 1 - 2sin2A


Q. The vectors and have components

Calculate the size of angle ABC

Today we will be learning to solve trigonometric equaons with double angles.

Homework due Tuesday

Fix Formula!!

Examples:

1. Solve sin 2x˚ - 3sin x˚ = 0 for 0 ≤ x ≤ 360.

Solving equations with double angle formulae

Sin2A = 2SinACosA



2. Solve sin 2x - cos x = 0 for 0 ≤ x ≤ 2π.

Examples:

3. Solve cos 2x˚ + 3cos x˚ + 2 = 0 for 0 ≤ x ≤ 360.

Solving equations with double angle formulae

Sin2A = 2SinACosA



Q1. The functions f and g, defined on a suitable domain, are given by

f(x) = and g(x) = x - 3

(a) Find k(x) = f(g(x)) in its simplest form

(b) State a suitable domain for k

Q2. Solve 2sin3x0 - 1 = 0 for 0 ≤ x ≤ 180

Today we will be continuing to solve equations with double angle formulae.

Homework due tomorrow!

Mixed Addition Formulae Questions

Example:

Ex. 11J Heinemann Book

Q6. Show that cos LOM =

N

O M

H

L

150mm

200mm

Documents

S56 (5.3) Addition Formulae.notebookmissdeely.weebly.com/.../higher_addition_formulae.pdf · S56 (5.3) Addition Formulae.notebook February 09, 2016 1. Daily Practice 4.2.16 Today