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Master 45-45-90 Triangle Rules: Solve Expressions Easily

Grade 12 Math: Master Advanced Concepts & Skills

Geometric explorations

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Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Conics - Parabola

Conics - Circle

Conics - Ellipse

Conics - Hyperbola

Graphical representations of polynomial, logarithmic, exponential, and sinusoidal functions

Graphing exponential functions

Graphing transformations of exponential functions

Graphing logarithmic functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Regression analysis

Equation of the best fit line

Combinatorics

One to one functions

Combining transformations of functions

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Factorial notation

Path counting problems

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Function notation (advanced)

Composite functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Inverse functions

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

Operations with functions

Inequalities of combined functions

Inequalities of Combined Functions

Even and odd functions

Difference quotient: applications of functions

Odds, probability, and expected value

Applications of linear relations

What is a polynomial?

Classifying Polynomials

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

Probability of independent events

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Reading and drawing Venn diagrams

Probability with Venn diagrams

Financial planning

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

Binomial theorem

Finance: Compound interest

Finance: Compound Interest

Finance: Future value and present value

Permutation vs. Combination

We&apos;ve got you covered with our complete help for Grade 12 math, whether it&apos;s Ontario curriculum, <a href="https://www.alberta.ca/writing-diploma-exams.aspx">Diploma exam</a> (Alberta), <a href="http://www.edu.gov.mb.ca/k12/assess/tests/index.html">Provincial test</a> (Manitoba) or <a href="https://www.saskatchewan.ca/residents/education-and-learning/departmental-exams">Departmental exam</a> (Saskatchewan).

Aligned with your class or textbook, you will get grade 12 math help on topics like Trigonometric identities, Vectors, Permutations and Combinations, Matrices, Polynomial functions and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 12 math questions. Then, strengthen your understanding with tons of grade 12 math practice. 

All our lessons are taught by experienced Grade 12 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Foundations of Mathematics 12

math

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Intro

Ex. 1

- Hi, welcome to special 
[inaudible 00:00:02]. 
So we're dealing with special triangles, okay. So, here it says, "If the angle is 45 degrees, find the exact value of the following expressions." So, what we have here is this. We've got the, a three and a sine square of the theta here. So, if this is 45 degrees, what happens is there's a three and you take the sine and there's a square here and this is the theta 45. Now, don't worry about the square right now. And you're not squaring the 45. See, the problem with the trig is that they like to put the square here, rather than actually here. Technically, this thing right here, is actually saying this: sine 45 and then you put a square sign like that. But they don't do it this way. They actually put it here, I don't know why. So, let's go ahead and figure this out, but you can use your calculator but remember, 45 degrees is one of a special triangle. So, what that means is, you have 90 degrees, right. And this is 45 and this is 45. So, remember, if you happen to have this special triangle, the ratio's going to be one, one and a root two for the hypotenuse. So, what that means is, you're going to have the sine 45 is going to turn out to be opposite over hypotenuse like that. So, you're going to get yourself one over root two for this part right here or this part right here. So, I'm just going to continue to work right here. Sine 45 is just one over root two and then you square that. So, if you square the one, just let me do a little work here a little bit. Square root of one is double one. If you take the root to square it, you get the two. And three times one over two, the final answer is just three over two. And that is your final answer for this one. Thanks for watching.