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

CC.HSF.TF.A.1

auto-gen

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

CC.HSF.TF.A.2

Unit circle

CC.HSF.TF.A.3

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Find the exact value of trigonometric ratios

CC.HSF.TF.B.5

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

CC.HSF.TF.B.6

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Two-step Linear Equations LHS

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

CC.HSF.TF.B.7

Evaluating inverse trigonometric functions

CC.HSF.TF.C.8

Pythagorean identities

CC.HSF.TF.C.9

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

CC.HSG.C.B.5

CC.HSG.CO.A.1

Line symmetry

Angles in a circle

Chord properties

Circles and circumference

Circle properties

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

CC.HSG.SRT.C.6

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

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

CC.HSG.SRT.C.7

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

CC.HSG.SRT.C.8

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

CC.HSG.SRT.D.10

Law of sines

Ambiguous case: SSA triangles

Law of cosines

CC.HSG.SRT.D.11

Applications of the sine law and cosine law

CC.HSG.SRT.D.9

Area of triangles: 1/2 a*b sin(C)

math

Intro

Ex. 1

<p>- Hi, welcome to special<br />
[inaudible 00:00:02].<br />
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.</p>
