Using the COSINE Rule.

Slides:

Advertisements

Similar presentations

The Cosine Rule A B C a b c. The Cosine Rule A B C a b c.

Advertisements

Mixed examples – which rule to use? Study each of these diagrams and determine which rule to use – Sine Rule or Cosine Rule? If Cosine Rule, which version?

Whiteboardmaths.com © 2004 All rights reserved

Starter a 6 c A 49° 96° 1.Use the Law of Sines to calculate side c of the triangle. 2.Now find the Area of a Triangle.

Trigonometry 2 Aims Solve oblique triangles using sin & cos laws Objectives Calculate angles and lengths of oblique triangles. Calculate angles and lengths.

The sine rule When the triangles are not right-angled, we use the sine or cosine rule. Labelling triangle Angles are represented by upper cases and sides.

© T Madas. 6 m 8 m Finding the hypotenuse x = x2= x = x2= x2 100 = x2= x2 = x= x = x= x 10 x = m 13 m Finding one of the shorter.

STARTER x x In each triangle, find the length of the side marked x.

Sin and Cosine Rules Objectives: calculate missing sides and angles is non-right angles triangles.

Find the angle between the forces shown if they are in equilibrium.

AREA OF A TRIANGLE. Given two sides and an included angle:

Starter Draw a right angled triangle, where the two shorter sides are 7cm and 13cm, and measure the hypotenuse 7cm 13cm ?

Sine and Cosine Rule- Which One to Use?. Two Sides and Included Angle To find side x, use the …. cosine rule To find angle Y, use the … sine rule 7cm.

Review of Angles. Acute Angle – Angle less than 90 degrees Right Angle – Angle that is exactly 90 degrees.

Area of Triangles Non Right-Angled Triangle Trigonometry By the end of this lesson you will be able to explain/calculate the following: 1.Area of Right-Angled.

We are now going to extend trigonometry beyond right angled triangles and use it to solve problems involving any triangle. 1.Sine Rule 2.Cosine Rule 3.Area.

H) select and use appropriate trigonometric ratios and formulae to solve problems involving trigonometry that require the use of more than one triangle.

Mr Barton’s Maths Notes

Trigonometry Angles Sides and Lengths Questions Questions Finished

The Sine and the Cosine © T Madas.

Dealing with Vectors Forces are used as an example though rules apply to any vector quantities.

Starter A triangular pyramid is made from baked bean tins

C2 TRIGONOMETRY.

The Cosine Rule.

Credit Revision Chapters

9-3: Other Identities.

Lesson Starter Q1. Calculate

Warm Up: Revision of Pythagoras and Trigonometry

Finding sin, cos, and tan.

Trigonometry 4. Sine and Cosine Rules

Using the Pythagoras Theorem.

Starter Jane is 40. Chris is 10. Chris is ¼ of Jane’s age.

What are Reference Angles?

Area of triangles.

Awkward Triangle.

GCSE: Non-Right Angled Triangles

Sine Rule and Cosine Rule.

Triangle Starters Pythagoras A | Answers Pythagoras B | B Answers

The graph of sin θ Teacher notes Trace out the shape of the sine curve and note its properties. The curve repeats itself every 360°. Also, –1 < sin.

Sine Rule and Cosine Rule Joan Ridgway.

Sine and Cosine Rule revision

Multiple-Angle and Product-Sum Formulas

a b c a2 = b2 + c2 Remember the rule. Coordinates and Pythagoras

Sine Rule and Cosine Rule Joan Ridgway.

Trigonometry Terrace Find out the angle CAB using Trigonometry.

L.O. Trigonometry All will be able to remember the sine rule

Area of triangles.

Warm-up: Find sin(195o) HW : pg. 501(1 – 18).

Y10 Triangle Starters Pythagoras A | Pythagoras A Answers

Sine Rule and Cosine Rule Joan Ridgway.

Starter Sketch a regular pentagon

We are Learning to…… Use The Cosine Law.

Forces What did you pull ?.

Unit 9. Day 17..

Trigonometric Functions

Trigonometry 2 L.O. All will be able to remember the sine rule

Trigonometry 2 L.O. All pupils can find missing sides on right angled triangles All pupils can find missing angles in right angled triangles.

Let’s think about the function f() = sin 

LT: I can use the Law of Sines and the Law of Cosines to find missing measurements on a triangle. Warm-Up Find the missing information.

Warm Up – 2/27 - Thursday Find the area of each triangle.

What can your remember about triangles?

Welcome GCSE Maths.

Unit 3: Right Trigonometric Ratios

The Cosine Rule. A B C a b c a2 = b2 + c2 -2bccosAo.

Grade 12 Essential Math Geometry and Trigonometry Unit

Aim: How do we solve trig equations using

The Cosine Rule. A B C a b c a2 = b2 + c2 -2bccosAo.

Presentation transcript:

Using the COSINE Rule

Quick starter … answer these cos(x) = 6 ÷ 9 = 2/3 x = cos-1(2/3) x = 48.19° 62 + b2 = 92 b2 = 81 - 36 b = √45 b = 6.71cm H 9cm 9cm O b Q 1 Q 2 x° 6cm 6cm A cos(33°) = 11.3 ÷ y y = 11.3 ÷ cos(33°) y = 13.47cm A O 11.3 cm Q 3 33° y H

 From the formula sheet on exams … Seems to combine Pythagoras and cosine formula

The Cosine Rule DOESN’T HAVE TO BE RIGHT-ANGLED TRIANGLE

Eg 1 B y (a) 7.9 cm (c) 116° C A 6.5 cm (b) y2 = 6.52 + 7.92 – 2 x 6.5 x 7.9 x cos(116°) y2 = 42.25 + 62.41 – 102.7 x (-0.438371146…) y = √149.6807168… = 12.23 cm (2dp)

Eg 2 B 12 cm (a) 6 cm (c) y° C A 8 cm (b) 122 = 82 + 62 – 2 x 8 x 6 x cos(y°) 144 = 100 – 96 x cos(y°) (-100) 44 = (– 96) x cos(y°) 44 = cos(y°) 96 ÷(-96) - y = cos-1( 44 ) = 117.28° (2dp) 96 -

cos (90°) = 0 Remember … y = cos (θ) y 1 0.5 -0.5 -1 θ -360 -270 -180 -90 0 90 180 270 360 y 1 0.5 -0.5 -1 cos (90°) = 0 Remember … y = cos (θ)

62 + b2 = 92 b2 = 81 - 36 b = √45 b = 6.71cm 9cm b Q 1 6cm C 92 = b2 + 62 – 2 x b x 6 x cos(90°) 9cm (a) b 81 = b2 + 36 – 12 x b x 0 (b) 81 = b2 + 36 B A 6cm b2 = 81 - 36 b = √45 b = 6.71cm (c)