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

PC20.1

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Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

PC20.10

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Sigma notation

PC20.11

Graphing reciprocals of linear functions

Graphs of rational functions

Graphing reciprocals of quadratic functions

PC20.2

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Multiplying radicals

Rationalize the denominator

PC20.3

Solving rational equations

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

Applications of rational equations

PC20.4

Unit circle

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

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

PC20.5

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

PC20.6

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

PC20.7

Transformations of quadratic functions

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

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

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

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

Completing the square

Completing the Square

PC20.8

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

PC20.9

Solving quadratic inequalities

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Pre-Calculus 20

Number Sense

math

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.