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

Describe linear relations through patterns, graphs, tables, equations, interpolation and extrapolation

auto-gen

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

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>

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)

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Function notation

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Solve problems using sine law and cosine law, excluding ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Solve problems involving triangles, quadrilaterals, and regular polygons

Similar triangles

Similar polygons

Isosceles and equilateral triangles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Demonstrate understanding of 2-D and 3-D transformations

Combining transformations of functions

Line symmetry

Rotational symmetry and transformations

Enlargements and reductions with scale factors

Scale diagrams

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Demonstrate understanding of measuring instrument limitations and solve problems

Upper and lower bound

Upper and Lower Bound

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

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

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

Analyze puzzles and games involving logical reasoning using problem-solving techniques

Direct variation

Identifying direct variations

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Solve problems involving vehicle acquisition by buying, leasing, or leasing to buy

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

Finance: Future value and present value

Critique small business options considering expenses, sales, profit or loss

Marginal profit, and maximizing profit & average profit

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

Inverse variation

Joint and combined variation

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Demand, revenue, cost & profit

Marginal revenue, and maximizing revenue & average revenue

Marginal cost, and minimizing cost & average cost

Analyze and interpret problems involving probability

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

Law of total probability

Law of Total Probability

Probability of a randomly selected employee meeting a sales target

Probability of a randomly selected driver being involved in an accident

Probability of a randomly selected customer making a purchase

Probability of a randomly selected person being overweight

Bayes' rule

Bayes" Rule

Bayes rule

Bayes" rule

Bayes' Rule

Probability with Venn diagrams

Solve problems involving measures of central tendency

Frequency distribution and histograms

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Stem and leaf plots

The Leaf and Stem of Numbers

Recognizing the Leaf and Stem of Numbers

Recognizing The Leaf And Stem of Numbers Leaf

Recognizing The Leaf And Stem of Numbers Stem

Reading Stem and Leaf Plots — Median

Reading Stem and Leaf Plots — Range

stem and leaf plots Range

Reading Stem and Leaf Plots

Reading Stem and Leaf Plots — Mean

Reading Stem and Leaf Plots — Mode

Frequency polygons

Shapes of distributions

Analyze and describe percentiles

Bivariate, scatter plots and correlation

Regression analysis

Equation of the best fit line

Apprenticeship and Workplace Mathematics 12 (MAT631K)

Measurement

Number

Probability

math

Ex.1

Ex.2

intro

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.