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Law of Cosines: When to Use It and How to Apply It

Analyze puzzles and games that involve numerical reasoning using problem-solving strategies

Arithmetic sequences

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Arithmetic series

Arithmetic series formula

Geometric sequences

Arithmetic mean vs. Geometric mean

Model and draw 3-D objects and their views

Surface area of 3-dimensional shapes

Characteristics of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Applications of quadratic functions

Draw and describe exploded views component parts and scale diagrams of simple 3-D objects

Similar triangles

Similar polygons

Converting from general to vertex form by completing the square

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Completing the square

Completing the Square

Solve problems that involve personal budgets

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Applications of rational equations

Applications of inequalities

Demonstrate understanding of financial institution services used to access and manage finances

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Demonstrate understanding of slope as rise over run and rate of change by solving problems

Direct variation

Identifying direct variations

Inverse variation

Joint and combined variation

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Rate of change

Solve problems by applying proportional reasoning and unit analysis

Solving rational equations

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Solve problems that require manipulation and application of formulas related to slope and rate of change

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Transformations of quadratic functions

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Quadratic function in vertex form: y = a(x-p)^2 + q

Solve problems that involve scale

Enlargements and reductions with scale factors

Scale diagrams

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Simplifying complex fractions

Demonstrate understanding of linear relations by recognizing patterns trends graphing creating tables

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Applications of linear relations

System of linear equations

System of linear-quadratic equations

Graphing linear inequalities in two variables

Graphing systems of linear inequalities

Solve problems that involve two and three right triangles

Unit circle

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Grade 11 Essential Mathematics (30S) - Half Course 4

Develop critical thinking skills

Develop spatial sense

Develop an understanding of managing money

Develop proportional reasoning

Develop spatial sense related to triangles

math

Ex.1

Bearing problem with ambiguous case using law of sines

Ex.2

Finding an angle using the cosine rule given all three sides

intro

Intro to the law of cosines and its derivation from the Pythagorean theorem

There are times when the Law of Sines cannot solve the triangle because we encounter a triangle with either one of the following two scenarios &ndash; SAS (Side-angle-side), or SSS (Side-Side-Side). What should we do then? We consider using the <a href='[[glossary.html|{"keyword":"Law of Cosines"}]]'>Law of Cosines</a>, which is another formula that models the relationship between the sides and the angles of any triangle. In this section, we will learn about the concept and the usage of the Law of Cosines, also known as the Cosines Rule.